Question

A Person can row a distance of 4 km upstream in 1 hour 20 minutes and can row back to the starting point in just 24 minutes. How much time (in hours) will he take to row 13 km in still water?

• A. 3
• B. $2$\frac{1}{2}$$
• C. 3$\frac{1}{2}$
• D. 2

Answer 1

Answer:

D. 2

Given:

Time taken to cover a distance of 4 km upstream = 1 hour 20 minutes = $\frac{4}{3}hours$

Time taken to cover a distance of 4 km downstream = 24 minutes

Concept Used:

The direction along the stream is called downstream.

The direction against the stream is called upstream.

Formula Used:

Distance = Speed $\times$ Times

Downstream speed of the boat = Speed of boat + Speed of stream

⇒ D_s = x + y

Upstream speed of the boat = Speed of boat - Speed of stream

⇒ Us = x - y

Calculation:

Let Speed of boat in still water be x km/hr & speed of stream be y km/hr

According to the question,

$⇒\frac{4}{(x-y)}=\frac{4}{3}$

⇒ x – y = 3      ----(1)

$⇒\frac{4}{(x+y)}=\frac{24}{60}$

⇒ x + y = 10     ----(2)

Add equation (1) and equation (2) we get,

⇒ 2x = 13

⇒ x = $\frac{13}{2}km/hr$

Time taken to row 13 km in still water = Distance covered/Speed of boat

Time taken = 13 $\div$ $\frac{13}{2}=2hrs$

∴ The time taken to row 13 km in still water is 2 hours.