The speed of a boat in still water is 8 km/hr. If the boat can go 15 kms downstream and 22 km upstream in 5 hours, then calculate the speed of the stream.

Explanation

Let the speed of the stream be x km/hr.
In still water the speed of the boat is 8 km/hr.
`:.` the speed of boat in down-stream =(8+x) km/hr and in up-stream =(8-x) km/hr.
As per question, `(15)/(8+x)+(22)/(8-x)=5`
or, `(15(8-x)+22(8+x))/((8+x)(8-x))=5or,(120-15x+176+22x)/(64-x^(2))=5`
or, `7x+296=320-5x^(2)or,5x^(2)+7+296-320=0`
or, `5x^(2)+7x-24=0...........(1)`
Comparing (1) with `ax^(2)+bx+c=0` we get, `a=5,b=7,c=-24`.
`:.x=(-7pmsqrt((7)^(2)-4xx5xx(-24)))/(2xx5)` [by Sreedhar Acharya's formula]
`=(-7pmsqrt(49+480))/(10)=(-7pmsqrt(529))/(10)`
`=(-7pm23)/(10)=(-7+23)/(10)`
`=(16)/(10)` [Taking +sign] `=(8)/(5)=1(3)/(5)`.
Hence the speed of the stream is `1(3)/(5)` km/hr.