Question

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. If he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?

• A. $\frac{7}{3}$
• B. $\frac{4}{3}$
• C. $\frac{5}{3}$
• D. $\frac{8}{3}$

Hint:

Use relative speed equations for downstream and upstream, then solve the simultaneous equations.

Answer 1

The Correct Option is C

Let rowing rate in still water = $r$, current speed = $c$. Downstream speed = $r+c$, upstream speed = $r-c$. Time difference condition: $\frac{12}{r-c} - \frac{12}{r+c} = 6$. Doubling rowing rate $\Rightarrow$ downstream speed = $2r + c$, upstream = $2r - c$, time difference = 1. Solving the system gives $c = \frac{5}{3}$.