Question

Hølla guys .
For all brainlics .

Solve this :-

A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Best of luck .

Answer 1

▶ Answer :-

→ 6 km/hr .

▶ Step-by-step explanation :-

→ Speed of the motorboat in still water = 18 km/hr .

→ Let the speed of the stream be x km/hr .

→ Then, speed upstream = ( 18 - x ) km/hr .

→ Speed downstream = ( 18 + x ) km/hr .

→ Time taken to go 24 km upstream = $\bf \frac{24}{(18-x)}$ hours .

→ Time taken to return 24 km downstream = $\bf \frac{24}{(18+x)}$ hours .

$\huge \pink{ \mid \underline{ \overline{ \tt Solution :- }} \mid}$

$\begin{lgathered}\sf \because \frac{24}{(18 - x)} - \frac{24}{(18 + x)} = 1. \\ \\ \sf \implies \frac{1}{(18 - x)} - \frac{1}{(18 + x)} = \frac{1}{24} . \\ \\ \sf \implies \frac{(18 + x) - (18 - x)}{(18 - x)(18 + x)} = \frac{1}{24} . \\ \\ \sf \implies \frac{2x}{(324 - {x}^{2}) } = \frac{1}{24} . \\ \\ \sf \implies324 - {x}^{2} = 48x. \\ \\ \sf \implies {x}^{2} + 48x - 324 = 0. \\ \\ \sf \implies {x}^{2} + 54x - 6x - 324 = 0. \\ \\ \sf \implies x(x + 54) - 6(x + 54) = 0. \\ \\ \sf \implies(x - 6)(x + 54) = 0. \\ \\ \sf \implies x - 6 = 0. \: \: \green{or} \: \: x + 54 = 0. \\ \\ \sf \implies x = 6 \: \: \green{or} \: \: x = - 54. \\ \\ \huge{ \orange{ \boxed{ \boxed{ \tt \therefore x = 6.}}}} \\ \\ \bigg( \tt \because speed \: of \: the \: stream \: cannot \: be \: negative. \bigg)\end{lgathered}$

✔✔ Hence, the speed of the stream is 6 km/hr ✅✅ .

Answer 2

Speed of boat = 18 km/hr

let the speed of stream be x km/hr.

during downstream,

speed = 18 + x

distance = 24 km

time taken = D/S = 24/(18+x)

during upstream,

speed = 18-x;

distance = 24 km

time taken = D/S = 24/(18-x)

according to the question,

24/(18-x)  -   24/(18+x)  = 1

⇒ (24(18+x)-24(18-x)) / (18-x)(18+x) = 1

⇒ (24 * 18 + 24x - 24 * 18 + 24x)/(18*18 - x²) = 1

⇒ 48x / (324 - x²) = 1

⇒ 48x = 324 - x²

⇒ x² + 48x - 324 = 0

on solving it,

⇒ x² - 6x + 54x -324 = 0

⇒ x(x-6) +54(x-6) = 0

⇒ (x+54)(x-6) = 0

case 1:

x=-54

not applicable as speed cannot be negative.

case 2:

x=6 km/hr

∴ Speed of stream = 6 km/hr

hope it helps you...

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