Math CentralQuandaries & Queries


Question from Christine, a student:

In a car race, the speed of one car is 120kph and the other car is 105 kph. If the faster car finished the race 20 mins before the slower one, what was the distance of the race?

Hi Christine,

The key here is to use the fact that distance equals time times rate.

Suppose that the faster car travels the distance $d$ kilometers to the end of the race in $t$ hours. Hence

\[d = t \times 120.\]

20 minutes is one third of an hour so how long does it take the slower car to travel the same distance? Write this as an equation. Since $d$ is the same in both equations you can write one equation for $t.$ Solve for $t.$ What is $d?$


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