# Question

Hi everyone

can help with this question ,thank you!

Omar and Mike were racing on a cross country motor race at an average speed of 140km/h and 120km/h respectively. At 8am, Omar was 45km ahead of Mike. 45 mins later, Omar’s car broke down and he discontinued the race.

(a) How far was Omar ahead of Mike when Omar’s car broke down?

(b) At what time did Mike pass the point where Omar’s car broke down?

Source: Assessment

Omar is 20km/h faster than Mike.

Every hour, Omar travels 20km further away from Mike.

Every 15 minutes, Omar travels (20 ÷ 4) = 5km further away from Mike.

At 8am, Omar is 45km ahead of Mike.

(a) After 45 mins, Omar would be (45 + 5 × 3) = 60km ahead of Mike.

When Omar’s car broke down at 8:45 am, Mike was 60 km behind.

Since Mike’s speed was 120 km/h, he would need half an hour to cover the 60km.

(b) Mike passed Omar 30 mins after 8:45 am -> 9:15 am

0 Replies 1 Like ✔Accepted Answer

(a)
140 – 120 = 20 (km that Omar travelled more than Mike for every hour)
45/20 = 2.25 (time taken for Omar to be 45 km ahead of Mike)
2.25 h ——-> 45 km
3 h ——-> (45/2.25) x 3 = 60

(b)
60/120 = 1/2
8.45 am ——- 1/2 h ——- 9.15 am

Ans : (a) 60 km; (b) 9.15 am.

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