Question

$\displaystyle\huge\red{\underline{\underline{QUESTION}}}$

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


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Answer 1

Answer:

$\huge\underline\mathfrak\red{Solution}$

Let the speed of the stream be x km/hr

Speed of the boat in still water =24 km/hr

Speed of the boat in upstream =(24−x) km/hr

Speed of the boat in downstream =(24+x) km/hr

Distance between the places is 32 km.

Time to travel in upstream =

24–x

d

hr

Time to travel in downstream =

24+x

d

hr

Difference between timings =1 hr

Time of upstream journey = Time of downstream journey +1 hr

Therefore,

24–x

32

=

24+x

32

+1

24–x

32

−

24+x

32

=1

(24−x)(24+x)

768+32x−768+32x

=1

64x=576–x

2

x

2

+64x−576=0

On factoring, we get

(x+72)(x−8)=0

So, x=−72 or 8 (speed of the stream cannot be negative)

Therefore, speed of stream is 8 km/hr.

Answer 2

Answer:

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