Question

At its usual rowing rate, a boat can travel 32 km upstream in 2 hours more than it takes to cover the same distance in downstream. If speed of boat in still water is reduced to half of it's initial speed then it takes 8 hours more to cover a distance of 20 km in upstream than in downstream. What is the reduced speed of boat in still water?

1. 12 km/hr
2. 8  km/hr
3. 5km/hr
4. 6 km/hr
5. 4 km/hr

Answer 1

Correct Answer - Option 4 : 6 km/hr

Given:

A boat can travel 32 km upstream in 2 hours more than in downstream.

The difference in time = 2 hours

Formula Used:

Upstream = Still water speed - Current speed

Downstream = Still water speed + Current speed

Distance = speed × time

Calculation:

Let the speed of still water be 2x km/hr.

Let the speed of current be y km/hr.

According to the question,

 \(\frac{{32}}{{2x - y}} - \frac{{32}}{{2x + y}} = 2\)

⇒ 16(2x + y) - 16(2x - y) = 4x² - y²

⇒ 4x² - y² = 32y       ----(I)

After reducing still water speed be x.

Then, The difference in time = 8 hours

⇒ \(\frac{{20}}{{x - y}} - \frac{{20}}{{x + y}} = 8\)

⇒ 20(x + y) - 20(x - y) = 8(x² - y²)

⇒ x² - y² = 5y 

⇒ y² = x² - 5y       ----(II)

By solving equation (I) and (II)

x = 6 km/hr and  y = 4 km/hr

Therefore, the reduced speed of boat in still water is 6 km/hr.