Question

A car starts from point P on a circular track and an SUV starts from point Q, which is 600 meters ahead of P in the direction of motion. The car's speed is 15 m/s, and the SUV's speed is 10 m/s. The circumference of the track is 1.5 km. How much distance will the car have traveled when it first overtakes the SUV?

• A. 900 m
• B. 1200 m
• C. 1500 m
• D. 1800 m

Answer 1

Answer:

D. 1800 m

Circumference of track = 1.5 km = 1500 m
Initial gap (Q ahead of P) = 600 m

Both move in same direction, so relative speed:

$15 - 10 = 5 \text{ m/s}$

Time to first catch up:

$\frac{600}{5}=120\text{ seconds}$

Distance travelled by the car in this time:

$15\times120=1800\text{ m}$

Since the track is circular, after 1500 m the car completes 1 full lap and continues 300 m more.

So, distance traveled when it first overtakes = 1800 metres.