Math, asked by Janeeta, 1 year ago

A streamer travels 90 km downstream in the same time as it takes to travel 60 km upstream. If the speed of the steamer is 5 km/h, find the speed of the steamer in still water.

Answers

Answered by Anonymous

the speed of the steamer in still water is 25km/h

Janeeta: May I know the steps that takes up to the answer 25km/h please.

Anonymous: let, the speed of the steamer is x km/h. in downstream it goes( x+5)km/h. in upstream it goes (x-5)km/h. in downstream it goes 90 km in 90/(x+5) h. in upstream it goes 60km in 60/(x-5) h. as two time is equal so , 90/(x+5)=60/(x-5). or,3/(x+5)=2/(x-5). or, 3x-15=2x+10. or, 3x-2x=10+15. or, x=25.

Janeeta: Thank you

Anonymous: well come

Answered by Shaizakincsem

We will assume the speed of the boat as B and the Speed of current as C

speed of downstream = (B + C) Km/h

speed of upstream = (B - C) Km/h

We are given,

time = distance /speed

so, time taken in downstream + time taken in upstream = 12 h

90/(B + C) + 70/(B - C) = 12 ----(1)

Time taken in downstream = 9 h

72/(B + C) = 9

B + C = 8 km/h---------(2) , put it in equation (1)

90/8 + 70/(B -C) = 12

45/4 + 70/(B - C) = 12

70/(B - C) = 12 - 45/4 = 3/4

B - C = 280/3 km/h -------(3)

Now we will solve both equations (2) and (3),

2B = 280/3 + 8 => B = 140/3 + 4 = 152/3 km/h

now we will Put B in equation (2) ,

C = 8 - 152/3 = (24-152)/3 = -128/3 km/h

here , negative sign shows that Current is just opposite side of our assumption

So speed of current = -128/3 km/h

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