Question

A boat goes 12 km upstream and 40 km downstream in 8 hrs. it can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream. ​

Answer 1

Answer:

hello buddy

explanation:

Let the speed of the boat in still water be x km/hr.

Let the speed of the stream be y km/hr.

So, the speed of the boat upstream = x-y

The speed of the boat downstream = x+y

Since

Therefore,

and,

Suppose,

So, the equations become 8 = 12p + 40q

and 8 = 16p + 32q

Now, solve the equations for p and q by elimination method and replace p by x-y and q by x+y.

You get, x-y = 4

x+y = 8

Solve these equations for x and y by elimination method. So, the speed of the boat in still water is 6 km/hr. and the speed of the stream is 2 km/hr.

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Answer 2

Answer:

let the speed of boat be x and stream

speed =distance/time

so, time=distance /speed

1st case: 12/(x-y)+40/(x+y)=8

2nd case: 16/(x-y)+32/(x+y)=8

let 1/(x-y) be p and 1/(x+y) be q

ao, eq. 12p+40q=8

4(3p+10q)=8

3p+10q=2 ...(1)

16p+32q=8

16(p+2q)=8

p+2q=1/2 ...(2)

multiplying eq (2) by3

3(p+2q=1/2)

3p+6q=3/2 ....(3)

eliminating eq. (3) from eq.(1)

3p+10q=2

3p+6q=3/2

- - -

4q=1/2

q=1/8

p+2q=1/2

p+2×1/8=1/2

p+1/4=1/2

p=1/2-1/4

p=1/4

p=1/(x-y)

1/4=1/(x-y)

x-y=4 ........(4)

q=1/(x+y)

1/8=1/(x+y)

x+y=8 ..........(5)

eliminating eq (4) from eq. (5)

x+y=8

x-y=4

2x=12

x=6km/hr

x-y=4

6-y=4

y=2km/hr

so, speed of boat =6km/hr

speed of stream=2km/hr