Question

Arun's swimming speed in still water is 5 km/hr. He swims between two points in a river and returns to the starting point. He took 20 minutes more upstream than downstream. If the stream speed is 2 km/hr, the distance between the points is:

• A. 3 km
• B. 1.5 km
• C. 1.75 km
• D. 1 km

Answer 1

Answer: (C)

1.75 km

Answer 2

We are given:

Speed in still water $v = 5 \text{ km/hr}$,
Speed of stream $u = 2 \text{ km/hr}$,
Additional time taken upstream = 20 minutes = $\frac{1}{3}$ hours.

The effective speeds are:

Speed Upstream = $v - u = 5 - 2 = 3 \text{ km/hr}$,
Speed Downstream = $v + u = 5 + 2 = 7 \text{ km/hr}$.

Let the distance between the two points be $d \text{ km}$. The time taken for upstream and downstream travel is:

Time Upstream = $\frac{d}{3}$,
Time Downstream = $\frac{d}{7}$.

The difference in time between upstream and downstream travel is:

$\frac{d}{3} - \frac{d}{7} = \frac{1}{3}$.

Simplify the equation:

$\frac{7d - 3d}{21} = \frac{1}{3}$,
$\frac{4d}{21} = \frac{1}{3}$.

Multiply through by 21:

$4d = 7$, $d = \frac{7}{4} = 1.75 \text{ km}$.

Thus, the distance between the two points is 1.75 km.