Question

A motor boat whose speed is 20 km/hr in still water, takes 1 hr more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

100 km/hr is the answer

Answer 2

Answer:

Let the speed of stream be x.

Then,

Speed of boat in upstream is 20 ‒ x

In downstream, speed of boat is 20 + x

According to question,

Time taken in the upstream journey ‒ Time taken in the downstream journey = 1 hour

$\implies\tt \dfrac{48}{20 - x} - \dfrac{48}{20 + x} = 1 \\\\\\\implies\tt\dfrac{20 + x - 20 + x}{{20}^{2} -{x}^{2}} = \dfrac{1}{48} \\\\\\\implies\tt \dfrac{2x}{400 -{x}^{2}} = \dfrac{1}{48}\\\\\\\implies\tt 2x\times 48 = 400 -{x}^{2}\\\\\\\implies\tt {x}^{2} + 96x - 400 = 0\\\\\\\implies\tt {x}^{2} + 100x - 4x - 400 = 0\\\\\\\implies\tt x(x + 100) - 4(x + 100) = 0\\\\\\\implies\tt (x - 4)(x + 100) = 0\\\\\\\implies\tt \green{x = 4} \quad or \quad \red{x =-100}$

⠀

∴ Speed of the Stream will be 4 km/hr.