UPCAT Mathematics practice question 23: A car leaves a terminal at 60 km/h. One hour later a second car leaves the same terminal along the same road at 80 km/h. How long after the second car departs will it overtake the first?
Correct answer
B. 3 hours
The first car has a 60 km head start, and the second gains 20 km/h. It closes the gap in 60 ÷ 20 = 3 hours.
The question
A car leaves a terminal at 60 km/h. One hour later a second car leaves the same terminal along the same road at 80 km/h. How long after the second car departs will it overtake the first?
- Option A: 2 hours
- Option B: 3 hoursCorrect
- Option C: 4 hours
- Option D: 5 hours
Why B is correct
The first car has a 60 km head start, and the second gains 20 km/h. It closes the gap in 60 ÷ 20 = 3 hours.
Why the other options are wrong
- A 2 hours
- Divides the 60 km head start by 30 rather than by the 20 km/h closing speed.
- C 4 hours
- This is the time measured from when the *first* car left, not from the second car's departure, which is what the question asks.
- D 5 hours
- Uses the difference in speeds incorrectly, treating the gap as 100 km.