Question

The speed of a boat in still water is 8km/h. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Answer 1

let X be the speed of the stream
speed of the boat in still water = to 8 km /hr

thus the speed of the boat in upstream =(8-x) km/hr
speed of the boat in downstream =(8+x )km/hr

$time = \frac{distance}{speed}$
the time taken by boat to cover 15 km
$= \frac{15}{8 - x} hour$
the time taken by boat to cover 22 km
$= \frac{22}{8 + x} hour$
total time =5hrs (given)
$\frac{15}{8 - x} + \frac{22}{8 + x} = 5 \\ 15(8 + x) + 22(8 - x) = 5(8 - x)(8 + x) \\ 120 + 15x + 176 - 22x = 5(64 - {x}^{2} ) \\ 296 - 7x = 320 - {5x}^{2} \\ {5x}^{2} - 7x - 24 = 0 \\ 5x(x - 3) + 8(x - 3) = 0 \\ (5x + 8)(x - 3) = 0 \\ 5x + 8 = 0 \: orx - 3 = 0 \\ x = \frac{ - 8}{5} = 0 \: or \: x = 3 \\ x = 3$
x=3

since speed cannot be negative
Therefore speed of steam is 3km/hr

Hope it helps to you.

Answer 2

Answer:

3 KM/h

Step-by-step explanation:

let X be the speed of the stream

speed of the boat in still water = to 8 km /hr

thus the speed of the boat in upstream =(8-x) km/hr

speed of the boat in downstream =(8+x )km/hr

the time taken by boat to cover 15 km

the time taken by boat to cover 22 km

total time =5hrs (given)

x=3

since speed cannot be negative

Therefore speed of steam is 3km/hr