Question

A motorboat traveling with a current can go 120 km in 4 hours. Against the current, it takes 6 hours to go the same distance. Find the speed of the motorboat and speed of the current.

Answer 1

The speed of motorboat in still water is 25 km/hr and speed of current is 5 km/hr

Solution:

Given that, motorboat traveling with a current can go 120 km in 4 hours

In water, the direction along the stream is called downstream

Let us find the downstream speed

Downstream distance = 120 km

time taken in downstream = 4 hours

The speed is given by formula:

$speed = \frac{distance}{time}$

$\text{ Downstream speed } = \frac{120}{4} = 30$

Thus downstream speed = 30 kilometer per hour

Against the current, it takes 6 hours to go the same distance

The direction against the stream is called upstream

Let us find upstream speed

Upstream distance = 120 km

time taken in upstream = 6 hours

$\text{Upstream speed } = \frac{120}{6} = 20$

Thus upstream speed is 20 kilometer per hour

Formula to use:

If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

$\text{Speed in still water } = \frac{1}{2}(a+b) \text{ kilometer per hour }\\\\\text{Speed of stream } = \frac{1}{2}(a-b) \text{ kilometer per hour }$

Therefore,

$\text{Speed of boat in still water } = \frac{1}{2}(30+20) = 25\\\\\text{Speed of stream } = \frac{1}{2}(30-20) = 5$

Thus speed of motorboat in still water is 25 km/hr and speed of current is 5 km/hr