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

Answer 2

The speed of motorboat in still water = 25 km/h

The speed of current = 5 km/h

A motorboat traveling with a current can go 120 km in 4 hours.

So the hourly speed of motorboat with the current = 120/4 = 30 km/h

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

So the speed of motorboat against the current = 120/6 = 20 km/h

We have to find out  the  speed of the motorboat and speed of the current.  

$\rm Let \; the\; speed\; of \; motorboat \; in \; still\; water\; be\; x \\The \; speed \; of\; current\; be\; s$

From the figure attached for both the cases of boat travelling with the direction of current and against the direction of current  we can write the equations (1) and (2) as formulated below

$\rm x +s =30 ..............(1)\\s-x= -20...........(2)$

Adding equations (1) and (2) we get

$\rm 2\times s =10 \\s =5 \; km/h$

On putting value s in equation (1) we get

$\rm x = 30-5 = 25\; km/h$

So we can conclude that speed of motorboat in still water = 25 km/h

The speed of current = 5 km/h

For more information please refer to the link given below

https://brainly.com/question/19260269