Question

A motor boat covers a certain distance downstream in a river in five hours. It covers the same distance upstream in five hours and a half. The speed of the water is $1.5$km.hr. The speed of the boat in still water is ___________.

• A. $30$km/hr
• B. $30.5$km/hr
• C. $31.5$km/hr
• D. $20$km/hr

Answer 1

Answer: (C)

$31.5$km/hr

Let the distance covered be s,speed of boat in still water be x km/hr .

we k.n.t distance $=$ speed x time

Given time taken for downstream is 5 hrs.

net speed of boat in downstream is (x+1.5) ($\because$ water helps in moving)

$s=(x+1.5)\times 5$....................(i)

Given time taken for downstream is 5.5 hrs.

net speed of boat in downstream is (x-1.5) ($\because$ water retard the motion)

$s=(x-1.5)\times 5.5$...............(ii)

Solving equations (i) and (ii)

$s=(5x+7.5)=(5.5x-8.25)$

$\Rightarrow 5x+7.5=5.5x-8.25$

$\Rightarrow 5.5x-5x=7.5+8.25$

$\Rightarrow 0.5x=15.75$

$\therefore x=\frac{15.75}{0.5}=31.5$

$\therefore$ Speed of boat in still water is $31.5$ km/hr