Rate of the boat in still water is 47 km/hr and rate of the current is 14 km/hr
Solution:
Given that,
A motorboat travels 165 Kilometers in 5 hours going up stream.
It travels 305 kilometers going downstream in the same amount of time
Therefore,
Upstream distance = 165 km
Upstream time = 5 hours
Find upstream speed:
[tex]speed = \frac{distance}{time}\\\\speed = \frac{165}{5}\\\\speed = 33[/tex]
Thus upstream speed is 33 km per hour
Downstream distance = 305 km
Downstream time = 5 hours
Find downstream speed:
[tex]speed = \frac{305}{5}\\\\speed = 61[/tex]
Thus downstream speed is 61 km per hour
If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then
Speed downstream = u + v km/hr
Speed upstream = u - v km/hr
Therefore,
u + v = 61 ---- eqn 1
u - v = 33 ----- eqn 2
Add eqn 1 and eqn 2
u + v + u - v = 61 + 33
2u = 94
u = 47
Substitute u = 47 in eqn 1
47 + v = 61
v = 61 - 47
v = 14
Thus rate of the boat in still water is 47 km/hr and rate of the current is 14 km/hr
