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

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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