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

#### Video Explanation

#### Explanatory Answer

Speed of motorboat in still water = 24 km/hr

Let speed of stream be x km/hr

Upstream speed of boat = (24 – x)km/hr

Time taken to travel 32 km upstream = \\frac{32}{24 - x})hr

Downstream speed of boat = (24 + x) km/hr

Time taken to travel 32 km downstream = \\frac{32}{24 + x})

The boat takes an hour longer to travel upstream than to travel downstream

i.e., \\frac{32}{24 - x}) = \\frac{32}{24+x}) + 1

\\frac{32}{24 - x}) = \\frac{32 + 24 + x}{24 + x})

\\frac{32}{24 - x}) = \\frac{56 + x}{24 + x})

Cross multiply and solve for x

32 (24 + x) = (24 – x)(56 + x)

32 × 24 + 32x = 24 × 56 + 24x - 56x - x^{2}

32 × 24 + 32x = 56 × 24 – 32x - x^{2}

x^{2} + 64x + 24 (32 - 56) = 0

x^{2} + 64x - 24 × 24 = 0

x^{2} + 72x – 8x – 576 = 0

{x + 72) (x - 8) = 0

x = - 72 or x = 8

Speed of stream cannot be negative.

So, speed of stream = 8 km/hr