Thabo ran the Two Oceans Marathon in 1hour less than Jodi. Thabo’s speed was 2,8 km/h faster than Jodi’s speed. If the marathon was 56km long, what was Jodi’s speed and what was Jodi’s time?

Question

The question is a quadriceps equation word problem that is found in a Grade 10 mathematics textbook.

Answer 1

Let Jodi's speed be J kph. Jt=56 km, where t is Jodi's time to complete the marathon. Thabo's speed is J+2.8 kph. Thabo's time=t-1 hrs. So (t-1)(J+2.8)=56 km, therefore Jt=(t-1)(J+2.8)=Jt+2.8t-J-2.8.

2.8t=J+2.8. But t=56/J so we can substitute for t:

2.8(56/J)=J+2.8, 156.8=J²+2.8J, J²+2.8J-156.8=0=(J-11.2)(J+14).

So J=11.2kph. Jodi's speed is 11.2kph.

CHECK

J=11.2 so t=56/11.2=5hrs. Thabo's speed is 11.2+2.8=14kph, and Thabo's time=56/14=4hrs, one hour less than Jodi. So the facts check out.

We could have substituted for J instead of t, using J=56/t:

2.8t=56/t+2.8, 2.8t²=56+2.8t, 2.8t²-2.8t-56=0, t²-t-20=(t-5)(t+4), so t=5hrs. Then Jodi's speed=56/5=11.2kph. The quadratic in this method is easier to solve but the method requires an extra step to find Jodi's speed knowing the time.​