Question

20. A motorboat goes downstream in river and covers a distance between two
coastal towns in 5 hours. It covers this distance upstream in 6 hours. If the speed
of the stream is 3 km/hr, find the speed of the boat in still water​

Answer 1

Answer:

The required speed of the boat is 33km/hr.

Step-by-step explanation:

Given :

A motorboat goes downstream in river and covers a distance between two  coastal towns in 5 hours.

It covers this distance upstream in 6 hours.

The speed  of the stream is 3 km/hr.

To Find :

The speed of the boat in still water​.

Solution :

Consider the :

The speed of the boat in still water as - y km/hr.

Therefore,

Speed of the boat downstream = (y + 3) km/hr.

Distance covered in 5 hrs = (y + 3) × 5.

Speed of the boat up stream = (y - 3) km/hr.

Distance covered in 5 hrs = 6(y - 3).

The distance between two coastal towns is fixed.

ATQ,

$\sf\\ \\\implies 5(y+3)=6(y-3)\\ \\ \implies 5y+15=6y-18\\ \\ \implies - y=-33\\ \\\implies y=33$

∴ The required speed of the boat is 33 km/hr.