Question

A boat takes 1.6hours longer to go 36kms up a river than down the river. If the speed of the water current is 4km per hour, what is the speed of the boat in still water?

Answer 1

Answer:

The speed of the boat in still water is 14 km/hr.

Step-by-step explanation:

Given : A boat takes 1.6 hours longer to go 36 kms up a river than down the river. If the speed of the water current is 4 km per hour.

To find : What is the speed of the boat in still water?

Solution :

Let the speed of the boat is x km/hr.

The speed of the river is 4 km/hr.

The upstream speed is (x-4) km/hr and downstream speed is (x+4) km/hr

We know, $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

It takes 1.6 hours longer to go 36 kms up a river than down the river.

According to question,

$\frac{36}{x-4}-\frac{36}{x+4}=1.6$

$\frac{36}{x-4}-\frac{36}{x+4}=\frac{16}{10}$

$\frac{9}{x-4}-\frac{9}{x+4}=\frac{2}{5}$

$9(x+4)-9(x-4)=\frac{2}{5}(x-4)(x+4)$

$9x+36-9x+36=\frac{2}{5}(x^2-16)$

$72=\frac{2}{5}(x^2-16)$

$x^2-16=180$

$x^2=180+16$

$x^2=196$

$x=14$

Therefore, the speed of the boat in still water is 14 km/hr.