# GCSE Foundation Maths question...?

### 1 Answer

- SamwiseLv 72 months ago
Car A completes 5 laps in 150 seconds.

The number of seconds car B takes to complete a lap must be a whole number

and a factor of 150 (so it completes a lap at 150 seconds after the start),

BUT it cannot be a factor of 30.

If it were, car B would complete a lap every time car A does.

Looking at the factorizations of 30 and 150, we can see that the only way

a factor of 150 cannot divide 30 is if it is a multiple of 25

so both the 5s in the factorization of 150 come into play.

So we are looking at possible factors of

2 * 3 * 5 * 5

that include the 5 * 5 part. These are

5 * 5 = 25 (Car B completes its sixth lap 150 seconds after the start.)

2 * 5 * 5 = 50 (Car B completes its third lap then.)

3 * 5 * 5 = 75 (Car B completes its second lap then.)

2 * 3 * 5 * 5 = 150 (Car B completes its first lap then.)

- Login to reply the answers