The speed of a boat in still water is 10km/h if it can travel 26 km downstream and 14 km upstream in the same time find the speed of the stream
Answers
Let the rate of the stream be x km/h.
The boat's rate when the river speeds up the boat by
adding its speed of x km/h to the boat's speed giving
10+x km/h.
The boat's rate when the river slows the boat down and
subtracts its speed of x km/h from the boat's speed
giving 10-x km/h.
Time = Distance/Rate
Downstream time = (Downstream Distance)/rate = 26/(10+x)
Upstream time = (Upstream Distance)/rate = 14/(10-x)
Those times are equal.
26/(10+x) = 14/(10-x)
Might as well divide both sides by 2
13/(10+x) = 7/(10-x)
Cross-multiply:
13(10-x) = 7(10+x)
130-13x = 70+7x
-20x = -60
x = 3 km/h
That's the answer. The rate of the river is 3 km/h. The story
is that he went down the river at 13 km/h for 26 km. for the
first 2 hours and came back at a slower 7 km/hr and only made
it 14 km of the way back when the second 2
Let the speed of the stream be y km/hr
Upstream- (y-10) km/hr
Downstream- (y+10) km/hr
time= distance÷ speed
t= 26/(y+10) and t=14/(y-10)
solve and equate the above given equations