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Question

# A man had to walk a certain distance. He covered one thirds of it at 5 kmph and the remaining distance at 6 kmph. If the total time taken is 40 minutes, then find the total distance.

A
3.75 km
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B
4 km
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C
5.25 km
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D
6.5 km
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Solution

## The correct option is A 3.75 kmWe know that, Speed=DistanceTime Let the distance be x. The man covers one third of it at 5 kmph. Hence, time taken is x3÷5=x15 hr. The remaining distance is x−x3=2x3 km. The man covers this distance at a speed of 6 kmph. Hence, time taken is 2x3÷6=x9 hr. Therefore, the total time taken is x15+x9 hr., which is equal to 40 minutes or 4060 hr. Hence, ⇒x15+x9=4060 ⇒ 5x+3x45=23⇒ 8x45=23⇒ x=2×453×8⇒ x=9024⇒ x=3.75 Thus, the total distance is 3.75 km.

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