Question

Scott trained for the marathon.

On day 1, he took 70 min to run 10 km.
On day 10, he took 2 h 40 min to run 20 km.
On day 20, he took 4 h 15 min to run 30 km.
a) What was Scott's running rate, in minutes per kilometre,
for each day?
i) Day 1 ii) Day 10 iii) Day 20
b) What do you think Scott's running rate, in minutes per
kilometre, might be for the 44 km of the marathon?
How long do you think it will take him? Explain.

Answer 1

See below

Explanation:

a)

Day 1

• 70 min for 10 km
• Rate = 70/10 = 7 min/km

Day 10

• 2h40 min for 20 km
• 2*60+40 = 160 min for 20 km
• Rate = 160/20 = 8 min/km

Day 20

• 4 h 15 min for 30 km
• 4*60 + 15 = 255 min for 30 km
• Rate = 255/30 = 8.5 min / km

b)

From the rate change we see:

• 1 min increase when the distance increases from 10 km to 20 km
• 0.5 min increase when distance increases from 20 km to 30 km

So we see 1 min increase per twice the distance increase

• With the same rate increase we can expect 1 min increase from 20 km to 40 km, which gives us the rate of 9 min/km
• With same logic we get 9.055 km/min rate for 44 km distance

Total time it takes:

• 9.055*44 = 398.42 min = 398.42*1/60 min = 6 h and 38.42 min