Arithmetic

Time, Speed & Distance

Medium

applied

A swimmer whose speed in swimming pool is 5 km/h, swims between two points in a river and returns back to starting point. He took 20 minutes more to cover the distance upstream than to cover downstream. If the speed of stream is 2 km/h, then the distance between two points is

1.75 km

0.233 km

35 km

0.25 km

✅ Correct Option: 1

The swimmer's speed in still water is 5 km/h and the stream's speed is 2 km/h.

Downstream speed (swimming with current) = 5 + 2 = 7 km/h

Upstream speed (swimming against current) = 5 - 2 = 3 km/h

Let the distance between the two points be $d$ km.

Time taken downstream = $\dfrac{d}{7}$ hours

Time taken upstream = $\dfrac{d}{3}$ hours

The upstream journey takes 20 minutes more than the downstream journey.

Converting 20 minutes to hours: $\dfrac{20}{60} = \dfrac{1}{3}$ hour

$\dfrac{d}{3} - \dfrac{d}{7} = \dfrac{1}{3}$

Finding the common denominator (LCM of 3 and 7 is 21):

$\dfrac{7d}{21} - \dfrac{3d}{21} = \dfrac{1}{3}$

$\dfrac{4d}{21} = \dfrac{1}{3}$

$4d \times 3 = 21 \times 1$

$12d = 21$

$d = \dfrac{21}{12}$

$d = \dfrac{7}{4}$

$d = 1.75$ km

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

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A swimmer whose speed in swimming pool is 5 km/h, swims between two points in a river and returns back to starting point. He took 20 minutes more to cover the distance upstream than to cover downstream. If the speed of stream is 2 km/h, then the distance between two points is

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