Question

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

Answer 1

Answer:

Given :-

• A motor boat whose speed is 18 km/h in still water takes 1 hours more to go 24 km upstream that to return downstream to the same spot.

To Find :-

• What is the speed of the stream.

Formula Used :-

$\clubsuit$ Time Formula :

$\bigstar \: \: \sf\boxed{\bold{Time =\: \dfrac{Distance}{Speed}}}\: \: \: \bigstar$

Solution :-

Let,

$\mapsto \bf Speed_{(Stream)} =\: x\: km/hr$

☆ Time Upstream :

Given :

• Speed = (18 - x) km/hr
• Distance = 24 km

According to the question by using the formula we get,

$\implies \bf Time =\: \dfrac{Distance}{Speed}$

$\implies \sf Time_{(Upstream)} =\: \dfrac{24}{18 - x}$

☆ Time Downstream :

Given :

• Speed = (18 + x) km/hr
• Distance = 24 km

According to the question by using the formula we get,

$\implies \sf Time =\: \dfrac{Distance}{Speed}$

$\implies \sf Time_{(Downstream)} =\: \dfrac{24}{18 + x}$

According to the question :

$\implies \bf \dfrac{24}{18 - x} - \dfrac{24}{18 + x} =\: 1$

$\implies \sf \dfrac{24(18 + x) - 24(18 - x)}{18^2 - x^2} =\: 1$

By doing cross multiplication we get,

$\implies \sf 24(18 + x) - 24(18 - x) =\: 18^2 - x^2$

$\implies \sf 432 + 24x - 432 + 24x =\: 324 - x^2$

$\implies \sf {\cancel{432}} {\cancel{- 432}} + 24x + 24x =\: 324 - x^2$

$\implies \sf 48x =\: 324 - x^2$

$\implies \sf x^2 + 48x - 324 =\: 0$

$\implies \sf x^2 + (54 - 6)x - 324 =\: 0$

$\implies \sf x^2 + 54x - 6x - 324 =\: 0$

$\implies \sf x(x + 54) - 6(x + 54) =\: 0$

$\implies \sf (x + 54)(x - 6) =\: 0$

$\implies \sf x + 54 =\: 0$

$\implies \bf x =\: - 54\: \: \: \bigg\lgroup \bf Speed\: can't\: be\: negetive \bigg\rgroup$

Or,

$\implies \sf x - 6 =\: 0$

$\implies \bf x =\: 6$

Hence, the value of x is 6 .

$\dag$ Required Speed of the Stream :

$\dashrightarrow \sf Speed_{(Stream)} =\: x$

$\dashrightarrow \sf\bold{Speed_{(Stream)} =\: 6\: km/hr}$

$\therefore$ The speed of the stream is 6 km/hr .

Answer 2

Answer:

Answer: The speed of the stream is 6 km/hr.

Let's explore the water currents.

Explanation:

Let the speed of the stream be x km/hr

Given that, the speed boat in still water is 18 km/hr.

Speed of the boat in upstream = (18 - x) km/hr

Speed of the boat in downstream = (18 + x) km/hr

It is mentioned that the boat takes 1 hour more to go 24 km upstream than to return downstream to the same spot

Therefore, One-way Distance traveled by boat (d) = 24 km .

Hence, Time in hour

Tupstream = Tdownstream + 1

[distance / upstream speed ] = [distance / downstream speed] + 1

[ 24/ (18 - x) ] = [ 24/ (18 + x) ] + 1

[ 24/ (18 - x) - 24/ (18 + x) ] = 1

24 [1/ (18 - x) - 1/(18 + x) ] = 1

24 [ {18 + x - (18 - x) } / {324 - x2} ] = 1

24 [ {18 + x - 18 + x) } / {324 - x2} ] = 1

⇒ 24 [ {2}x / {324 - x2} ] = 1

⇒ 48x = 324 - x2

⇒ x2 + 48x - 324 = 0

⇒ x2 + 54x - 6x - 324 = 0 ----------> (by splitting the middle-term)

⇒ x(x + 54) - 6(x + 54) = 0

⇒ (x + 54)(x - 6) = 0

⇒ x = -54 or 6

As speed to stream can never be negative, we consider the speed of the stream (x) as 6 km/hr.

Thus, the speed of the stream is 6 km/hr.