Question

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

Answer 1

QUESTION :-

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

SOLUTION :-

$\leadsto$ Let, the speed of stream be R km/hr.

$\implies$ then,

$\leadsto$ Speed of boat in upstream is 24 - R.

$\leadsto$in downstream, speed of boat is 24 + R.

$\implies$ NOW,

$\leadsto$ Time taken in the upstream journey - time taken in the downstream journey = 1 hour.

$\leadsto \: \frac{32}{24 - R} - \frac{32}{24 + R} = 1 \\ \\ \leadsto \: \frac{ \cancel{24 }+ R \cancel{- 24 }+ R }{(24) {}^{2} - R {}^{2} } = \frac{1}{32} \\ \\ \leadsto \: \frac{2R}{576 -R {}^{2} } = \frac{1}{32} \\ \\ \leadsto \: R { }^{2} + 64R - 576 = 0 \\ \\ \leadsto \: R {}^{2} + 72R - 8R - 576 = 0 \\ \\ \leadsto \: R \: (R + 72) - 8(R + 72) = 0 \\ \\ \leadsto \:( R - 8) \: \: (R + 72) = 0 \\ \\ \leadsto \: ∴ \: R \: = 8, \: - 72$

[ Since, we know that, speed can't be negative]

Hence, the speed of the stream is 8km/hr.

Answer 2

$\huge\underline\mathbb {SOLUTION:-}$

• Speed of boat = 24 km/hr
• Speed of stream = x km/hr

Upstream Journey:-

Time = $\mathsf {\frac{32}{24 - x}\:hrs}$

Downstream Journey:-

Time = $\mathsf {\frac{32}{24 + x}\:hrs}$

• Difference = 1

$\implies \mathsf {1 = \frac{32}{24 - x} - \frac{32}{24 + x} }$

$\implies \mathsf {\frac{1}{32} = \frac{1}{24 - x} - \frac{1}{24 + x} }$

$\implies \mathsf {\frac{1}{32} = \frac{24 + x - 24 + x}{24^2 - x^2}}$

$\implies \mathsf {24^2 - x^2 = 74x}$

$\implies \mathsf {x = 8\:or\:x = -72}$

• Speed cannot be negative.

$\therefore \underline \mathsf \blue {Speed\:of\:stream\:=\:8\:km/hr.}$