Question

A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30km upstream and 21 km downstream in 13 / 2 hours. Find the speed of boat in still water and also speed of the stream.

Its urgent.....

Answer 1

I hope u can understand

Answer 2

Answer:

The speed of boat in still water is 10 km/hr and the speed of stream is 4 km/hr

Step-by-step explanation:

Let the speed of boat in still water be x

Let the speed of stream be y

Upstream Speed = x-y

Downstream speed = x+y

Case 1 )

Distance of upstream = 24 km

Time = $\frac{Distance}{Speed}$

Time = $\frac{24}{x-y}$

Distance of down stream  = 28 km

Time = $\frac{Distance}{Speed}$

Time = $\frac{28}{x+y}$

Since we are given that total time is 6 hours  

So,  $\frac{24}{x-y}+\frac{28}{x+y}=6$  ---A

Case 2)

Distance of upstream =30 km

Time = $\frac{Distance}{Speed}$

Time = $\frac{30}{x-y}$

Distance of down stream  = 21 km

Time = $\frac{Distance}{Speed}$

Time = $\frac{21}{x+y}$

Since we are given that total time is 13/2 hours  

So,  $\frac{30}{x-y}+\frac{21}{x+y}=\frac{13}{2}$  ---B

Solve A and B

$\frac{24}{x-y}+\frac{28}{x+y}=6$

$]\frac{30}{x-y}+\frac{21}{x+y}=\frac{13}{2}$

Let $\frac{1}{x-y} = u$ and $\frac{1}{x+y} =v$

So, $24u+28v=6$ ----1

$30u+21v=\frac{13}{2}$   ---2

Multiply 1 with 5 and 2 with 4

$120u+140v=30$ ---5

$120u+84v=26$  ---6

Subtract 6 from 5

$120u+140v-120u-84v=30-26$

$140v-84v=4$

$56v=4$

$v=\frac{4}{56}=\frac{1}{14}$

Substitute the value of v in 5

$120u+140(\frac{1}{14})=30$

$120u+10=30$

$120u=20$

$u=\frac{20}{120} =\frac{1}{6}$

So, $\frac{1}{x-y} = \frac{1}{6}$ and $\frac{1}{x+y} =\frac{1}{14}$

$x-y=6$ --- 7 and $x+y=14$ ---8

Add 7 and 8

$x-y+x+y=6+14$

$2x=20$

$x=10$

Substitute in 8

$10+y=14$

$y=4$

Hence the speed of boat in still water is 10 km/hr and the speed of stream is 4 km/hr