Nisha flies from Mumbai to New York. The journey takes 16 hours 18 minutes.

(a) The flight departs at 11:50 Mumbai time. Mumbai is 10.5 hours ahead of New York. Find the local arrival time in New York. [2]

(b) The plane flies 12800 km. Calculate its average speed in km/h. [2]

Aryan leaves home at 11:40 and arrives at 14:18. Find the journey time in hours and minutes. [1]

Order these lengths from smallest to largest: \(0.03\text{ m},\ 2.9\text{ cm},\ 32\text{ mm},\ 0.00002\text{ km}\). [2]

A solid wooden cone has base radius 4 cm, height 12 cm and density \(0.74\text{ g/cm}^3\). Find its mass. [3]

(a) Convert 780 cm² into m². [1]

(b) Convert 0.037 m³ into cm³. [1]

Convert 9.5 m/s into km/h. [2]

A train is 1750 m long and travels at 55 km/h. A bridge is 480 m long. How long does the whole train take to completely cross the bridge? Give seconds to the nearest second. [3]

A map has scale 1:40000. Two villages are 37 cm apart on the map. Find their actual distance in kilometres. [2]

Every tram takes the same time between Newpoint and Westhill.

Complete the timetable. [2]

(a(i)) A car travels 50 km at 75 km/h. Find the time in minutes. [2]

(a(ii)) Another car travels 47 km to the nearest kilometre at 75 km/h to the nearest 5 km/h. Find the lower bound of its travel time in minutes. [3]

(b) A train travels 240 km: t minutes at 100 km/h, then(t+60) minutes at 110 km/h. Find its average speed for the whole journey. [6]

Convert \(7.51\text{ m}^2\) to cm². [1]

In 15 minutes Enzo swims 11.25 lengths, Rashid 18.75 and Blessy 20.

(a(i)) Find Enzo’s lengths as a percentage of their total. [2]

(a(ii)) Give Enzo:Rashid:Blessy in simplest form. [2]

Each pool length is 25 m.

(a(iii)(a)) Find Blessy’s average speed in m/s. [3]

(a(iii)(b)) Rashid continues at the same rate. Find the time for 5 km in hours and minutes. [4]

(a(iv)) Blessy swims for an hour; her lengths decrease by 5% each successive 15 minutes. Find her lengths in the final 15 minutes. [3]

(b) Adam swims 450 m to the nearest 25 metres in 10 minutes to the nearest minute. Find the minimum distance he swims in an hour at this rate. [3]

(a) Find the average speed in km/h of a runner who covers 100 m in 15 seconds. [2]

(b) An athlete runs for 45 minutes at 9.5 km/h, then another 8.1 km at 7.5 km/h. Find the average speed for the whole run. [3]

(c) A train of length p metres travels at v km/h. Write an expression for the time in seconds for the whole train to pass through a station of length q metres. [3]

A train journey starts at 21:43 and takes 8 hours 32 minutes.

Find the finishing time. [1]

A film lasts 2 hours 50 minutes and ends at 23:05.

Find its starting time. [1]

Convert 62 000 millimetres to kilometres. [1]

Tara’s train leaves at 06:48. The journey takes 12 hours 35 minutes. Find the arrival time. [1]

A journey starts at 21:15 one day and ends at 04:33 the next day. Find its duration in hours and minutes. [1]

Jason runs from 10:05 am until 1:02 pm. Find the time taken. [1]

Convert 300 m/min to km/h. [2]

A train at 108 km/h takes 7 seconds to pass completely through a station of length 120 m. Find the train length. [3]

Part of a bus timetable:

(a) Rashid boards the 09:20 bus at Abbots. When does it reach South Moor? [1]

(b) Annisa leaves home at 08:27, walks 25 minutes to Callet and catches the next bus to Centre Point. Find her total journey time in minutes. [2]

(c) Abbots to Centre Point is 29.4 km. Every bus takes the same journey time. Find its average speed in km/h. [2]

(d) All 56 seats are occupied; adults:children = 5:3. Adult tickets cost \$2.80; child tickets cost three quarters of that. Find the total ticket cost. [4]

A train journey starts at 23:40 and ends at 06:50 next day. Find the journey time. [1]

Marco works from 20:45 to 02:08 next day. Find the duration in hours and minutes. [1]

(a) A 45 cm × 30 cm × 42 cm cuboid is filled with 90.72 kg sand. Find density in kg/m³ (density = mass ÷ volume). [3]

(b) A bag contains 15 000 cm³ sand. Some fills a cylindrical hole, depth 30 cm and radius 10 cm. Find the percentage of the bag used. [3]

(c) Sand costs \$98.90 per tonne including 15% tax. Find the tax paid per tonne. [3]

(d) Raj pays 3540 rupees. Convert to dollars at \$1 = 70.8 rupees. [2]

Change 2.15 hours into minutes. [1]

Beatrice walks 1 km at 4 km/h, then 2 km at 4.5 km/h. Find the average speed of the whole journey. [3]

Hank flies from Los Angeles to Shanghai.

(a) The flight departs on Friday 22 July at 21:40 and takes 13 hours 35 minutes. Shanghai is 15 hours ahead of Los Angeles. Find the arrival day, date and local time in Shanghai. [3]

(b) The flight costs \$920. The exchange rate is \$1 = 6.87 Chinese yuan. Find the cost in yuan. [1]

A 105 m train takes 11 s to pass completely through a 225 m station. Find its speed in km/h. [3]

(a) A train journey of 5 hours 54 minutes starts at 09:15. Find its end time. [1]

(b) Its average speed is 80 km/h. Find the distance travelled. [2]

Convert457000 cm² to m². [1]

Karel travels London–Johannesburg–Windhoek.

(a) The first flight takes 11 h 10 min at average speed 813 km/h. Find its distance to the nearest 10 km. [3]

(b(i)) The whole journey takes 15 h 42 min and covers 10260 km. Find the average speed in km/h. [2]

(b(ii)(a)) The whole journey costs \$470. Find the distance travelled per dollar. [1]

(b(ii)(b)) Find the cost per 100 km, to the nearest cent. [2]

(c) Karel exchanges \$300 for 3891 Namibian dollars. Find the number of Namibian dollars for \$1. [1]

A water-filled pipe has circular cross-section of radius2.6 cm. Water flows at12 cm/s into a tank. Find the litres delivered in1 hour. [3]

Prague and Vienna are 254 km apart and have the same local time. A train leaves at 15:20 and arrives at 19:50 on the same day. Calculate its average speed. [2]

Brad travels from his New York home to Chamonix.

He leaves home at16:30 and takes a55-minute taxi journey to the airport at average18 km/h. His flight departs New York at22:15 and reaches Geneva at11:25 the next day, Geneva being6 hours ahead. The flight path is a circular arc of radius6400 km and sector angle55.5°. His bus leaves Geneva at13:00 and takes1 hour36 minutes at average65 km/h. Chamonix and Geneva have the same local time.

Find the overall average speed from home to Chamonix, in km/h. Show all working. [11]

Train timetable, all local times. Marseille is1 hour ahead of London; Ashford has London time.

(a(i)) Find the total London–Marseille journey time in hours and minutes. [2]

(a(ii)) London–Ashford is90 km. Find the average speed in km/h. [3]

(a(iii)) The train takes35 s to cross a bridge completely at90 km/h. Its length is95 m. Find the bridge length. [4]

(b) London–Marseille fares:

(b(i)) Simplify standard adult fare:child fare. [1]

(b(ii)) Find the percentage increase from standard to premier for an adult. [3]

(b(iii)) Adults:children=11:2, with220 adults. All children and70% of adults pay standard; remaining adults pay premier. Find total fares. [5]

(c) In2018 there were \(3.08\times10^5\) passengers, a12% decrease from2017. Find the2017 count in standard form. [3]

A water-filled pipe has cross-section 6 cm². Water flows at 1.2 m/s into a tank. Find the litres delivered in 1 hour. [4]

Cars A and B race on a circular 7.6 km track at constant speeds. A completes each lap in 2 min 40 s, B in 2 min 25 s.

(a) Find A’s speed in km/h. [3]

They start together at S.

(b(i)) Find the time until both are next at S together. Give minutes and seconds. [4]

(b(ii)) Find the distance A has travelled then. [2]

Liz runs 400 m in 65 seconds. Calculate her average speed. [1]

A car travels at 108 km/h for 20 seconds. Find its distance in metres. [3]

Change 6200 cm² into m². [1]

Amar cycles at 18 km/h for 55 minutes between two villages. Find their distance. [2]

Ahmed drives London to Cambridge, leaving at 07:45 and arriving at 10:17. Find the journey time in hours and minutes. [1]

A train leaves Zurich at 22:40 and arrives in Vienna at 07:32 the next day.

Work out the time taken. [1]

A car of length 4.3 m travels at 105 km/h and passes over a bridge of length 36 m.

Calculate the time, in seconds, to pass over the bridge completely. [3]

A train travels for \(m\) minutes at \(x\) metres per second.

(a) Find the distance in kilometres, in terms of m and x, in simplest form. [2]

(b) When \(m=5\), the train travels 10.5 km. Find \(x\). [2]

Fritz drives 381 km in 2 h 18 min, then 75 km at 30 km/h. Calculate his average speed for the whole journey. [4]

A car travels 1280 m at an average 64 km/h. Find the time in seconds. [3]

A doctor starts at 20:40 and finishes at 06:10 next day. Find the working time in hours and minutes. [1]

A water channel on horizontal ground has constant rectangular cross-sectional area 0.95 m². It is full, with water moving at 4 m/min. Calculate the volume flowing along the channel in 3 hours. [3]

A car travels at 56 km/h. How long does it take to travel 300 m? Give seconds to the nearest second. [4]

A bus company operates 06 00–24 00 from Saturday through Thursday, and 13 00–24 00 on Friday.

(a) Find the total operating hours per week. [3]

(b) Write Friday’s starting time in the 12-hour clock. [1]

A train travels 52 km in 65 minutes. Find its average speed in km/h. [2]

A water pipe has circular cross section of radius 0.75 cm. Water flows at 16 cm/s. Find the time for 1 litre to flow through it. [3]

Lisbon and Funchal have the same time. A plane leaves Lisbon at 08 30 and arrives in Funchal at 10 20. It leaves Funchal at 12 55; the return trip takes 15 minutes longer. Find its arrival time in Lisbon. [2]

Maria walks 1.8 km to school in 27 minutes, leaving home at 07 48.

(a(i)) State her arrival time. [1]

(a(ii)) Show her average speed is 4 km/h. [2]

Another day she cycles the 1.8 km at 15 km/h.

(b(i)) Find the percentage increase from 4 km/h to 15 km/h. [3]

(b(ii)) Find the percentage decrease in journey time from 27 minutes. [3]

(b(iii)) Cycling to a friend’s home takes 9 minutes, which is 36% of the walking time. Find the walking time. [2]

Christa has 52 music lessons, each lasting 45 minutes. Find the total time in hours. [2]

(a) Convert 60 m² to cm². [1]

(b) Convert 22 m/s to km/h. [2]

(a) Convert 144 km/h to metres per second. [2]

(b) A train 120 m long moves at 144 km/h under a bridge 20 m wide. Find the time for the whole train to pass, in seconds. [2]

Noma leaves Johannesburg at 18 45 and reaches Hong Kong after 13 hours 25 minutes. Hong Kong is 6 hours ahead.

(a) Find the local arrival time. [2]

(b) Sleeping : awake = 3 : 4. Find her sleeping time in hours and minutes. [2]

(c(i)) The journey is 10 712 km. Find the average speed. [2]

(c(ii)) The plane uses 1 litre of fuel per 59 metres. Find the litres used, in standard form. [4]

(d) The fare is R10 148, an 18% increase on last year. Find last year’s fare. [3]

A ferry leaves Helsinki at 17 30 on Tuesday. The journey takes 28 h 45 min. Find its arrival day and time. [2]

A lake has area 63 800 000 000 m². Give the area in km² to 2 significant figures. [2]

(a) A book costs €34.95 in Portugal and £27.50 in England. £1 = €1.17. Find the difference in pounds. [2]

(b) Planets are \(4.07\times10^{12}\) km apart. Light travels at \(1.1\times10^9\) km/h. Find the travel time in days and hours. [3]

A rectangle has length 9.3 cm and width 5.6 cm, each to 1 decimal place.

(c(i)) Give the lower bound of its length. [1]

(c(ii)) Find the lower and upper bounds of its area. [2]

A train travels from Paris to Milan.

(a(i)) It leaves at 20 28 and takes 9 h 10 min. Find its arrival time. [1]

(a(ii)) The distance is 850 km. Find its average speed. [2]

There are 640 passengers: 160 pay \$255, 330 pay \$190, and 150 pay \$180.

(b(i)) Find the mean ticket cost. [3]

(b(ii)) Men : women : children = 4 : 3 : 1. Show that there are 240 women. [2]

(b(iii)) 240 is 60% more than the previous day’s number of women. Find that number. [3]

(c) The train is 210 m long. It passes a 340 m station at 180 km/h. Find the time to pass completely through. [3]

1 astronomical unit (AU) is approximately \(1.496\times10^8\) km. Earth is 1 AU from the Sun.

(a) Complete the table. [3]

Light travels at approximately 300 000 km/s.

(b(i)) Find the Sun–Earth travel time, in seconds. [2]

(b(ii)) Find the Sun–Pluto travel time, in minutes. [2]

(c) Find one light year in kilometres in standard form. Use 365 days per year. [3]

(d) How many AU equal one light year? [2]

The Martinez family drives 92 km to Seatown in 1 hour 25 minutes.

(a(i)) They leave at 07:50. Find their arrival time. [1]

(a(ii)) Find the average speed in km/h. [2]

(a(iii)) They stop for 10 minutes. Express this as a percentage of 1 hour 25 minutes. [1]

(a(iv)) 92 km is 15% more than the distance from Seatown to Deecity. Find that distance. [3]

They spend \$150 in the ratio fuel:meals:gifts = 11:16:3.

(b(i)) Show that \$15 is spent on gifts. [2]

(b(ii)) Two gifts are bought; the first costs \$8.25. Find first gift cost : second gift cost in simplest form. [2]

A train leaves Barcelona at 21:28 and takes 10 hours 33 minutes to reach Paris.

(a) Find its arrival time the next day. [1]

(b) The distance is 827 km. Find the average speed in km/h. [3]

(a) The café opens for 100 hours each week. Find Saturday’s opening time. [2]

(b) A later Sunday closing increases weekly opening hours by 4%. Find the new Sunday closing time. [1]

A ship travels at 22 knots. One knot is 1.852 km/h. Convert the speed to m/s. [3]

A car at 108 km/h takes 1 second to pass a building. Find the building’s length in metres. [2]

Convert 64 m² to mm², in standard form. [2]

Convert 252 km/h to m/s. [2]

One second is \(10^6\) microseconds. Convert \(3\times10^{13}\) microseconds to minutes, in standard form. [2]

Priyantha runs 10 km in 55 minutes 20 seconds. Find average speed in km/h. [3]

An 80 cm × 90 cm card is all used to make 40 mm × 15 mm rectangular cards. Find their number. [2]