Question : The speed of a boat in still water is 8km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Doubt by Gauri
Solution :
Let the speed of the stream be = x km/h
Speed of boat in still water = 8 km/h
Total speed of boat during upstream = (8-x) km/h
Time taken by boat in going 15 km upstream
t1=15/(8-x) [∵ Time = Distance/Speed ]
t1=15/(8-x) [∵ Time = Distance/Speed ]
Total speed of the boat during downstream
= (8+x) km/h
Time taken by boat in going 22 km downstream
t2= 22/(8+x)
= (8+x) km/h
Time taken by boat in going 22 km downstream
t2= 22/(8+x)
ATQ
t1+t2 = 5
Solving Quadratic Equation by Splitting The Middle Term
5x²-7x-24=0
5x²-(15-8)x-24=0
5x²-15x+8x-24=0
5x(x-3)+8(x-3)=0
(5x+8)(x-3)=0
(5x+8)=0
5x=-8
x=-8/5
But speed of the stream can't be -ve.
so, x≠-8/5 (Rejected)
(x-3)=0
x=3
Hence, the required speed of the stream is 3 km/h
5x²-7x-24=0
5x²-(15-8)x-24=0
5x²-15x+8x-24=0
5x(x-3)+8(x-3)=0
(5x+8)(x-3)=0
(5x+8)=0
5x=-8
x=-8/5
But speed of the stream can't be -ve.
so, x≠-8/5 (Rejected)
(x-3)=0
x=3
Hence, the required speed of the stream is 3 km/h