Car A leaves city C at 5 pm and it is driven at a speed of 40 km/h. Two hours…
2024
Car A leaves city C at 5 pm and it is driven at a speed of 40 km/h. Two hours later another car leaves city C and it is driven in same direction as car A. In how much time car B be 9 km ahead of car A, if the speed of car B is 60 km/h.
- A.
3 hr 45 min
- B.
4 hr 15 min
- C.
4 hr 42 min
- D.
4 hr 27 min
Attempted by 471 students.
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Correct answer: D
Answer: 4 hr 27 min
Let t be the time (in hours) after car B starts.
Speed of car A = 40 km/h; speed of car B = 60 km/h. Relative speed = 60 − 40 = 20 km/h.
When car B starts, car A has already been driving for 2 hours, so head start = 40 × 2 = 80 km.
Car B must gain that 80 km and go 9 km ahead, so total distance to gain = 80 + 9 = 89 km.
Time required = distance / relative speed = 89 / 20 = 4.45 hours = 4 hours + 0.45 × 60 minutes = 4 hours 27 minutes.
Therefore, car B will be 9 km ahead of car A 4 hours 27 minutes after car B starts (i.e., 4 hr 27 min).
Optional: Since car B starts at 7:00 pm (two hours after car A leaves at 5:00 pm), this occurs at 7:00 pm + 4:27 = 11:27 pm.