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?

Correct — D. The SUV starts 600 m ahead, so the car must first gain 600 m on it.

Same direction, so relative speed = 15 − 10 = 5 m/s
Time to gain 600 m = 600 ÷ 5 = 120 s
Car's distance = 15 × 120 = 1800 m → option (d)

Why the others are wrong

• (a)
  900 m — After 900 m (60 s) the car has gained only 5 × 60 = 300 m of the 600 m gap, so it is still behind the SUV.
• (b)
  1200 m — 1200 m is the SUV's distance in the 120 s (10 × 120), not the car's. The car, 5 m/s faster, covers 1800 m in that time.
• (c)
  1500 m — After one lap, 1500 m (100 s), the car has gained 5 × 100 = 500 m and is still 100 m behind the SUV.

On a circular track, two runners going the same direction close the gap between them at the difference of their speeds. Going opposite ways they would close it at the sum.

The gap is measured from the chaser forward to the one ahead. The SUV starts 600 m ahead, so the first overtaking comes when the car has gained 600 m, not a full lap.

The 1.5 km circumference only tells you where they meet: 1800 − 1500 = 300 m past P.

Key facts

• Same direction: relative speed = difference of speeds, 15 − 10 = 5 m/s.
• Time to overtake = gap ÷ relative speed = 600 ÷ 5 = 120 s.
• At 120 s the SUV has run 1200 m from Q, so both are 1800 m along the track from P, 300 m into the second lap.

Common traps

• Using a full lap (1500 m) as the gap: that applies only when both start from the same point.
• Adding the speeds (25 m/s) as if they ran towards each other, which gives 600 ÷ 25 = 24 s and only 360 m.
• Answering with the SUV's 1200 m when the question asks how far the car has gone.

No directly related past PYQ was found.