NEET Physics Question - Kinematics - Relative Motion in One Dimension

A boat takes two hours to travel 4 km down and 4 km up the river when the water is still. How much time will the boat take to make the same trip when the river starts flowing at 2 kmph?

2 hour

2 hour 40 minute

3 hour

3 hour 40 minute

Solution:

Let the boat's speed in still water be x kmph. Given $\frac{8}{x} = 2$ , we get x = 4 kmph.

With a 2 kmph current:

Downstream speed = 6 kmph, time = $\frac{4}{6} = \frac{2}{3}$ hours
Upstream speed = 2 kmph, time = $\frac{4}{2} = 2$ hours

Total time = $2 \frac{2}{3}$ hours or 2 hours 40 minutes.

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