Discussion

Question:

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

Explanation:

Let the speed of Rahul in still water be p and speed of current be q miles per hour.

$∴ \frac{12}{(p + q)} = \{\frac{12}{(p - q)} - 6\}$ ...(i)

$∴ \frac{12}{(2 p + q)} = \{\frac{12}{(2 p - q)} - 1\}$ ...(ii)

12_p − 12_q = 12_p+ 12_q − 6(p − q)(p + q)

On solving, we get,

4q = p² − q² … (iii)

24p – 12q = 24p + 12q – (4p² − q²)

On solving we get,

4p² − q² = 24q … (iv)

Solving (iii) and (iv), we get,

24q = 9q²

$q = \frac{8}{3}$

Hence, option (d).

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