Question

A river is flowing at a steady speed of 6 mph. The distance covered, rowing both upstream and downstream, is 30 miles. If the return journey while rowing upstream takes 2 hours more than the outward journey while downstream, then calculate the speed of rowing the boat in still water.

• A. 32 mph
• B. 8 mph
• C. 21 mph
• D. 15 mph

Answer 1

The correct option is D 15 mph

Let's take the speed of rowing the boat in still water as $u$ mph.

The steady speed of the river flow = 6 mph

Given, distance covered = 30 mi

Average speed downstream
$=(u+6)\text{mph}$

Therefore, time taken
$=\frac{\text{Distance covered}}{\text{Speed}}$
$=\frac{30}{u+6}\text{h}$

Distance in upstream motion = 30 mph
Average upstream speed $=(u-6)\text{mph}$

Therefore,
Time taken
$=\frac{\text{Distance covered}}{\text{Speed}}$
$=\frac{30}{u-6}\text{h}$

As the return journey takes 2 hours more than the downstream journey, we get:

$\frac{30}{u+6}+2=\frac{30}{u-6}$

$⟹\frac{30+2u+12}{u+6}=\frac{30}{u-6}$

$⟹\frac{2u+42}{u+6}=\frac{30}{u-6}$

$⟹(2u+42)(u-6)=30(u+6)$

$⟹2u^2-12u+42u-252=30u+180$

$⟹2u^2+30u-252=30u+180$

$⟹2u^2-252=180$

$⟹2u^2=180+252=432$

$⟹u^2=\frac{432}{2}$

$⟹u^2=216$

$⟹u=\sqrt{216}$

$⟹u=14.7\approx 15$

Hence, the speed of the rowing boat is approximately 15 mph.