Stage 9 - Q1 - 4 marks
The table gives clock times and cumulative distance travelled. Convert each time to elapsed minutes from the start. Identify the rest interval and the full journey distance.
Hint
Clock notation is hours and minutes, not decimal hours.
Stage 9 - Q2 - 5 marks
A rider cycles 11 km away from home in 40 min, rests 5 min, then returns on the same route in 25 min. Assume constant speed on each moving leg. Draw distance from home and total distance travelled against elapsed time on the same axes.
Hint
Both graphs are horizontal while the cyclist rests, but only distance from home falls on the return.
Stage 9 - Q3 - 5 marks
The same-route outward and return legs are each 10 km, taking 25 and 25 min. There is a 10-minute rest. Find average speed over the whole elapsed trip and over moving time only, to 1 decimal place.
Hint
Write explicitly which definition of time the average uses.
Stage 9 - Q4 - 5 marks
A cyclist goes 9 km from home in 35 min, rests 10 min, then returns at constant speed in 40 min. After \(65\) elapsed minutes, find distance from home and total distance travelled.
Hint
Subtract the outward time and rest before considering progress on the return.
Stage 9 - Q5 - 5 marks
A cyclist rides 8 km out at 12 km/h and the same 8 km back at 18 km/h, with no rest. Find the overall average speed and assess the arithmetic mean of the leg speeds.
Hint
Equal distances usually require unequal travel times.
Stage 9 - Q6 - 5 marks
Each day covers 14 km. Day A: 65 min moving, 20 min resting. Day B: 55 min moving, 40 min resting. Which is faster by moving-time average and which by elapsed-time average?
Hint
Compare like definitions: same distance, but two different denominators.
Stage 9 - Q7 - 5 marks
A cyclist goes 6 km from home in 40 min, rests 5 min, then returns at constant speed in 30 min. After \(60\) elapsed minutes, find distance from home and total distance travelled.
Hint
Subtract the outward time and rest before considering progress on the return.
Stage 9 - Q8 - 5 marks
A cyclist rides 5 km out at 15 km/h and the same 5 km back at 18 km/h, with no rest. Find the overall average speed and assess the arithmetic mean of the leg speeds.
Hint
Equal distances usually require unequal travel times.
Stage 9 - Q9 - 5 marks
A rider must complete 9 km out and 9 km back within 60 elapsed minutes. Outward speed is 18 km/h and return speed is 27 km/h. Find the longest permitted rest.
Hint
Add travel times before allocating the remaining deadline to a rest.
Stage 9 - Q10 - 8 marks
For equal outward and return distances d, a rider travels at speeds \(v+w\) and \(v-w\), where \(0<w<v\), with no rest. Derive the overall average speed and show it is below v. Evaluate it for v=20, w=5 km/h and d=10 km, and find the delay compared with travelling both legs at v.
Hint
The slower return leg takes longer; use total distance divided by total time.