Question

A boat has a speed of $15$m/hr in still water. In a stream that has a current of $5$ m/hr it travels a certain distance downstream and returns. The ratio of the average speed for the round trip to the speed in still water is:

• A. $\frac{5}{4}$
• B. $\frac{1}{5}$
• C. $\frac{8}{9}$
• D. $\frac{7}{8}$

Answer 1

Answer: (C)

$\frac{8}{9}$

$v_b$ = 15 m/hr (speed of boat)

$v_s$ = 5 m/hr (speed of stream)

Let the distance travelled = d m

Average speed = $\frac{totaldistance}{totaltimetaken}$

$=\frac{2d}{\left(\frac{d}{v_b+v_s}\right)+\left(\frac{d}{v_b-v_s}\right)}=\frac{2}{\frac{1}{20}+\frac{1}{10}}=\frac{40}{3}m/hr$

Ratio of the average speed to the speed in still water = $\frac{\frac{40}{3}}{15}=\frac{8}{9}$