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Question 15

Two cities Mathura and Agra, 48 kms apart, are located on the bank of River Yamuna. A motor boat
goes from Mathura to Agra and returns back as soon as possible. Yamuna flows at a speed of 6 km/hr.
The motorboat completes the trip from Mathura to Agra and back in not more than 6 hours. Assuming
the motorboat does nothalt at Agra, what should be the minimum speed of motorboatin still water?

Solution

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Let the river flow from Mathura to Agra. Let the speed of boat in still water be S kmph

Hence, if journey is to be done in 6 hours, then:
$$\frac{48}{S+6}+\frac{48}{S-6}=6$$

Solving this equation, we get: (S-18)(S+2) = 0 which gives us S = 18 kmph

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