Question

A motorboat goes downstream in river and covers a distance between two coastal towns in 6 hours. It covers this distance upstream in 8 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water. [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

Let the speed of the boat in still water $=xkm/hr$.

Speed of the boat downstream $=(x+2)km/hr$.

Time taken to cover the distance = 6 hrs

Therefore, distance covered in 6 hrs
$=(x+2)\times 6(Distance=Speed\times Time)$

Speed of the boat upstream $=(x-2)km/hr$

Time taken to cover the distance = 8 hrs.

Therefore, distance covered in 8 hrs $=8(x-2)$

Therefore, the distance between two coastal towns is fixed, i.e. same.

According to the question,

$6(x+2)=8(x-2)$

$\Rightarrow 6x+12=8x-16$

$\Rightarrow 6x-8x=-16–12$

$\Rightarrow -2x=-28$

$\Rightarrow x=14$

Required speed of the boat is 14 km/hr.