Arithmetic

Time, Speed & Distance

Medium

applied

A swimmer whose speed in still water is 6 km/hr, swims between two points in a river and returns to the starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/hr, then the distance between the two points is:

1 km

2.5 km

6.5 km

1.5 km

✅ Correct Option: 4

The swimmer's speed in still water is 6 km/hr and the stream speed is 3 km/hr.

When swimming downstream (with the current), the speeds add:

Downstream speed $= 6 + 3 = 9$ km/hr

When swimming upstream (against the current), the speeds subtract:

Upstream speed $= 6 - 3 = 3$ km/hr

The extra time taken upstream is 20 minutes.

Converting to hours:

$20$ minutes $= \dfrac{20}{60} = \dfrac{1}{3}$ hour

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

Time $= \dfrac{\text{Distance}}{\text{Speed}}$

Time to go upstream $= \dfrac{d}{3}$ hours

Time to go downstream $= \dfrac{d}{9}$ hours

The upstream time is $\dfrac{1}{3}$ hour more than the downstream time:

$\dfrac{d}{3} - \dfrac{d}{9} = \dfrac{1}{3}$

Converting to a common denominator of 9:

$\dfrac{3d}{9} - \dfrac{d}{9} = \dfrac{1}{3}$

$\dfrac{2d}{9} = \dfrac{1}{3}$

$2d \times 3 = 9 \times 1$

$6d = 9$

$d = \dfrac{9}{6}$

$d = 1.5$ km

Therefore, the distance between the two points is 1.5 km.

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Solution

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