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
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