Question

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

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Answer 1

Working out:

The given question is based on Boats & Streams and we have to find the speed of the stream with respect to given parameters.

GiveN:

• Speed of motorboat = 18 km/hr
• Distance to travel = 24 km
• Time taken more = 1 hour in upstream than in downstream.

We have to find the speed of the stream in this question.

Here we can frame equations by considering the spoed of the stream as any variable which would be easier for calculation. We know that, Time = Distance / Speed.

Let us consider:

• Speed of the stream be x

Then,

• Upstream speed = 18 - x

Upstream means against the direction of stream. Hence, the relative speed involves subtraction.

• Downstream speed = 18 + x

Downstream means along the direction of stream. Hence, the relative speed involves addition.

Now ATQ,

• Time taken to travel upstream = Time taken to travel downstream + 1 hr

Let's start solving....

$\sf{ \longrightarrow{ \dfrac{24}{18 - x} = \dfrac{24}{18 + x} + 1}}$

Taking LCM is RHS,

$\sf{ \longrightarrow{ \dfrac{24}{18 - x} = \dfrac{24 + 18 + x}{18 + x} }}$

$\sf{ \longrightarrow{ \dfrac{24}{18 - x} = \dfrac{42 + x}{18 + x} }}$

Cross multiplying,

$\sf{ \longrightarrow{24(18 + x) = (42 + x)(18 - x)}}$

$\sf{ \longrightarrow{432 + 24x = 756 + 18x - 42x - {x}^{2} }}$

$\sf{ \longrightarrow{432 + 24x = 756 - 24x - {x}^{2} }}$

$\sf{ \longrightarrow{ {x}^{2} + 48x -324 = 0}}$

Solving by middle term factorisation,

$\sf{ \longrightarrow{{x}^{2} + 54x - 6x - 324 = 0}}$

$\sf{ \longrightarrow{x(x + 54) - 6(x + 54) = 0}}$

$\sf{ \longrightarrow{(x + 54)(x - 6) = 0}}$

Then, x = -54 or 6

But x is the speed and speed can't be negative. So, value for x is 6 km /hr.

So, the required speed of the stream is:

$\huge{ \boxed{ \purple{ \bf{6 \: km {h}^{ - 1} }}}}$

And we are done !!

Answer 2

Answer:

Step-by-step explanation:Given parameters:

The speed of the motorboat in still water =18 kmph

Let us consider

The speed of the stream = s

Speed of boat upstream = Speed of a boat in still water – the speed of a stream

Speed of boat upstream = 18 – s

Speed of boat downstream = Speed of a boat in still water + speed of a stream

Speed of boat downstream = 18 + s

Time is taken for upstream = Time taken to cover downstream + 1

time =distance/speed

DistanceupstreamSpeedupstream=DistancedownstreamSpeeddownstream+1

24/ (18 – s) = [24/(18 + s)] + 1

24(18+s) = 24(18−s) + (18−s)(18+s)

s2 + 48s − 324 = 0

s2 + 54s − 6s − 324 = 0

(s+54)(s−6) = 0

s = 6,−54 but

s ≠−54

Since the speed of steam cannot be negative.

∴ s = 6km/hr