The speed of a boat in still water is 8km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Open in App

Solution

Let the speed of the stream be x km/hr.
Given, speed of the boat in still water = 8 km/hr
Therefore, speed in upstream = 8-x km/hr
Speed in downstream = 8+x km/hr
Now, time taken by boat to go 22 km downstream = $fraction numerator 22 over denominator 8 plus x end fraction k m divided by h r$
Time taken by boat to go 15 km upstream= $fraction numerator 15 over denominator 8 minus x end fraction k m divided by h r$
Total time taken by boat = 5 hrs
Total time taken = time taken in downstream + time taken in upstream.
Therefore,
$fraction numerator 22 over denominator 8 plus x end fraction plus fraction numerator 15 over denominator 8 minus x end fraction equals 5 rightwards double arrow fraction numerator 22 left parenthesis 8 minus x right parenthesis plus 15 left parenthesis 8 plus x right parenthesis over denominator left parenthesis 8 plus x right parenthesis left parenthesis 8 minus x right parenthesis end fraction equals 5 rightwards double arrow 176 minus 22 x plus 120 plus 15 x equals 5 left parenthesis 64 minus x squared right parenthesis rightwards double arrow 296 minus 7 x equals 320 minus 5 x squared rightwards double arrow 5 x squared minus 7 x minus 24 equals 0 rightwards double arrow 5 x squared minus 15 x plus 8 x minus 24 equals 0 rightwards double arrow 5 x left parenthesis x minus 3 right parenthesis plus 8 left parenthesis x minus 3 right parenthesis equals 0 rightwards double arrow left parenthesis 5 x plus 8 right parenthesis left parenthesis x minus 3 right parenthesis equals 0 rightwards double arrow x equals fraction numerator negative 8 over denominator 5 end fraction space o r space 3$

Since speed can not be negative hence the speed of stream is 3 km/hr.

Suggest Corrections

Similar questions

Q. A boat goes

15 k m

upstream and

22 k m

down stream in

15

hours. In

14

hours it can go

45

upstream and

55 k m

down stream. The speed of the boat in still water in

k m / h r

A boat can go 20 km upstream and 30 km downstream in 3 hrs. It can go 20 downstream and 10km upstream in 1 hrs 40 min . Find the speed of the boat in still water and speed of the stream.

Q. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

A man can row 40 km upstream and 55 km downstream in 13 hours. He can also row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the boat in still water and the speed of the current.

A boat goes 80 km upstream and 120 km downstream in 20 hours. In 15 hours, it can go 48 km upstream and 108 km downstream. Determine the speed of the boat in still water and that of the stream.

Join BYJU'S Learning Program