a boat in upstream covers 110km in same time as it covers 140km in downstream find speed of stream is what percent of the speed of the boat in still water
Answers
Let the speed of the boat be x km/h
Let the speed of the stream be y km/h
Upstream:
Speed = (x - y) km/h
Distance = 110 km
Time = Distance ÷ Speed
Time = 110 / (x - y)
Downstream:
Speed = (x + y) km/h
Distance = 140 km
Time = Distance ÷ Speed
Time = 140 / (x + y)
Given that the time taken is the same:
110/(x - y) = 140/(x + y)
110(x + y) = 140 (x - y)
110x + 120y = 140x - 140y
140x - 110x = 140y + 120y
30x = 250y
x = 25/3y
Find the percentage of the speed of the stream:
Percentage = (y ÷ 25/3y) x 100 = 12%
Answer: The speed of the stream is 12% the speed of the boat.
Let the speed of the boat is 'b' and speed of the stream is 's', therefore
For upstream, net speed = b-s, and we know that distance= speed * time , hence
110= (b-s)*t......eq 1
for downstream , net speed = b+s, hence,
140= (b+s)*t........eq 2
Dividing eq 2 by eq 1,
140/110 = (b+s)/(b-s)
=> 140*(b-s) = 110*(b+s)
=>140b -140s = 110b + 110s
=>30 b = 250 s
=> s/b = 30/250
Therefore speed of stream as % of speed of boat = s*100/b
= 30*100/250
=12%