Math, asked by shravanrajani1356, 7 months ago

Rohit can row his boat at 31 km/h in still water. But he takes 1 hour more to row upstream in comparison to downstream. If the distance of upstream or downstream is 15 km, find the speed of the stream.​

Answers

Answered by Ayushbhat
0

Answer:

Let the distance=d,

The speed of the boat =x and the speed of the water current=y.

UPSTREAM-

The relative speed of the boat & water current=x−y.

Then the time taken =

x−y

d

.

DOWNSTREAM-

The relative speed of the boat & water current=x+y.

Then the time taken =

x+y

d

.

So, by the given condition,

x−y

d

=2×

x+y

d

⟹2x−2y=x+y

⟹x=3y

y

x

=

1

3

i.ex:y=3:1

So the required ratio =3:1

Answered by bhagyashreechowdhury
0

Correct Question:

Rohit can row his boat at √31 km/h in still water. But he takes 1 hour more to row Upstream in comparison to downstream. If the distance of upstream or downstream is 15km, Find the speed of the stream.

Given:

Rohit can row his boat at √31 km/h in still water

He takes 1 hour more to row upstream in comparison to downstream

If the distance of upstream or downstream is 15 km

To find:

The speed of the stream

Solution:

Let "x" km/hr represent the speed of the stream.

The speed of the boat in still water = √31 km/hr

So,

The speed of the boat upstream = (√31 - x) km/hr

and

The speed of the boat downstream = (√31 + x) km/hr

We have the formula as:

\boxed{\bold{Time = \frac{Distance }{Speed} }}

Now, according to the question and based on the formula above, we can form an equation as:

\frac{15}{(\sqrt{31} -x)} - \frac{15}{(\sqrt{31} + x)}  = 1

\implies 15 [ \frac{{\sqrt{31} + x - \sqrt{31} + x } }{(\sqrt{31})^2 -(x)^2}]  = 1

\implies 15 [\frac{2x}{31 - x^2} ] = 1

\implies 30x = 31 - x^2

\implies x^2 + 30x  - 31 = 0

\implies x^2 + 31x  - x - 31 = 0

\implies x(x + 31) - 1 (x + 31) = 0

\implies (x + 31)(x - 1) = 0

\implies x = -31\: or\: 1

since speed of the stream cannot be in negative so we will ignore it

\implies \bold{ x = 1}

Thus, the speed of the stream is1 km/hr.

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