# A motorboat whose speed is 24km/hr in still water takes 1 hour more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.

Boat takes less time in downstream and more time upstream, to cover a certain distance.

## Answer: The speed of the stream is 8 km/hr.

Let's find the speed of the stream.

**Explanation:**

Given:

Speed of the motorboat in still water = 24km/hr

Let the speed of the stream be x km/hr

### For upstream:

Distance covered = 32 km

Speed of the motorboat moving upstream = (24 - x) km/hr

Time taken to cover the distance upstream = 32/(24 - x) hr

### For downstream:

Distance covered = 32 km

Speed of the motorboat moving downstream = (24 + x) km/hr

Time taken to cover the distance downstream = 32/(24 + x) hr

It is also mentioned in the question that the time taken to go upstream is 1 hour more than the time taken to go downstream.

Therefore, Upstream time - Downstream time = 1 hr

or, 32/(24 - x) - 32/(24 + x) = 1

or, 1/(24 - x) - 1/(24 + x) = 1/32

or, {(24 + x) - (24 - x)} / {(24 - x)(24 + x)} = 1/32

or, 2x/(576 - x^{2}) = 1/32

or, 1/(576 - x^{2}) = 1/64x

or, x^{2} + 64x - 576 = 0

Factorising this equation gives:

x^{2} + 72x - 8x - 576 = 0

or, x(x + 72) - 8(x + 72) = 0

or, (x + 72)(x - 8) = 0

or, x = 8, -72

Since, the speed cannot be negative, therefore, x = 8

### Thus, the speed of the stream is 8 km/hr.

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