Question

A boat covers 40 km upstream and 90 km downstream in 5 hr. it can also cover 60 km upstream and 60km downstream in 5 hr. the speed of the water current is

Answer 1

Let the speed of river be x km/h
Let the speed of boat be y km/h

Now as we know that "speed = distance/time"

We also write it as "time = distance/speed"

And we also know that if boat goes upstream then the speed will be "x-y km/h" and for downstream "x+y km/h"

Now,
As boat covers 40km upstream and 90km downstream in 5hr. By formula of
time=distance/speed

40/(x-y) + 90/(x+y) = 5

Also boatcovers 60km upstream and 60km downstream in 5hr.

60/(x-y) + 60/(x+y) = 5

Now,
Let 1/(x-y) = m and 1/(x+y)=n

Therefore, equations will be

40m+90n=5 -------------------(1)
60m+60n=5 -------------------(2)

In equation 2,

60m+60n=5

therefore, 12m+12n=1

12m=1-12n
m=(1-12n)/12 ---------------------(Result 1)

Putting Result 1 in Equation 1
40[(1-12n)/12] +90n = 5

40(1-12n) + 1080n = 60

40 - 480n + 1080n = 60

Taking 20 common from equation

2 - 24n + 54n = 3

30n=1

therefore, n=1/30 ---------(Result 2)
Putting Result 2 in Result 1

m = (1-12n)/12
m = [1-12(1/30)] / 12
m = 1/20 --------------(Result 3)

Now,
As we assumed that

1/(x-y) = m and 1/(x+y) = n

Putting value of m and n in these

1/(x-y) = 1/20

20=x-y
20+y=x -------------- (equation 3)

Same way

1/(x+y) = 1/30
30=x+y

By putting equation 3 in this

30 = 20 + y + y
2y = 10
y = 5km/h ------------------ Answer 1

Now Putting Answer 1 in Equation 3

20 + y = x
20 + 5 = x
x = 25km/h --------------------- Answer 2

Answer:- Speed of Water current is 25km/h
Speed of boat is 5km/h

Answer 2

Let speed of boat in still water be x km/hr & speed of water current be y km/hr;

Then

(40/(x-y)+90/(x+y))=5                       ....(1)

(60/(bx-y)+60/(x+y))=5                      ....(2)

on solving (1) and (2),

we get,  x=5y

Substitute this in any one of the equations and we will get,

y=5 km/hr

Therefore, speed of water current is 5 kmph.