Math, asked by deveshupadhyay277304, 3 months ago


36. A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours. In
the same time, it covers a distance of 12 km upstream and 36 km downstream. Find the
speed of the boat in still water and that of the stream.​

Answers

Answered by prasanthikuchipudi
9

Answer:

Speed of boat in still water m=8 km/hr

speed of boat that of the stream s=4km/hr

Step-by-step explanation:

Given,

A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours.

we know,

upstream=(m-s)km /hr

downstream=(m+s) km/hr

m is the speed of boat in still water

s is the speed of boat in stream

16 km upstream

24 km downstream

Speed=Distance/Time

Time=Distance/Speed

6 hrs=16/(m-s)+24/(m+s) -----(1)

In  the same time, it covers a distance of 12 km upstream and 36 km downstream.

6 hr=12/(m-s)+36/(m+s) ---------(2)

if the time is same then

Equating Eq(1) and (2)

16/(m-s)+24/(m+s)=12/(m-s)+36/(m+s)

16(m+s)+24(m-s)=12(m+s)+36(m-s)

16m+16s+24m-24s=12m+12s+36m-36s

40m-8s=48m-24s

8m=16s

m/s=16/8

m/s=2x/1x

substitute m and s in Eq (1)

6=16/(2x-1x)+24/(2x+1x)

6=16/x+24/3x

6=16/x+8/x

6x=24

x=4

m is 2x

2*4=8 km/hr

s is 1x=4 km/hr

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