Two cars start from the same point at the same time towards the same…
2026
Two cars start from the same point at the same time towards the same destination which is 420 km away. The first and second car travel at respective speed of 60 kmph and 90 kmph. After travelling for sometime the speeds of the two cars get interchanged. Finally the second car reaches the destination 1 hour earlier than the first . Find the time after which the speeds get interchanged ?
- A.
3 hr
- B.
4 hr
- C.
3.5 hr
- D.
4.5 hr
Attempted by 296 students.
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Correct answer: B
Solution: Find the time after which the speeds are interchanged.
Let t be the time (in hours) after which the speeds get interchanged.
Distance covered in t hours: first car = 60t km, second car = 90t km. Remaining distances: first = 420 - 60t, second = 420 - 90t.
After interchange, the first car travels the remainder at 90 km/h and the second at 60 km/h. Total times:
T1 (first car) = t + (420 - 60t)/90
T2 (second car) = t + (420 - 90t)/60
Given the second car reaches 1 hour earlier than the first, so T1 - T2 = 1. Compute the difference:
(420 - 60t)/90 - (420 - 90t)/60 = 1
Simplify: Multiply both sides by 180 to clear denominators:
2(420 - 60t) - 3(420 - 90t) = 180
840 - 120t - 1260 + 270t = 180
150t - 420 = 180
150t = 600 => t = 600/150 = 4 hours
Therefore the speeds are interchanged after 4 hours.