A boat takes 90 minutes less to travel 36 km downstream then to travel the same distance upstream.If the speed of the boat in still water is 10 kmph.What is the speed of the current?

since time = distance/speed,

36/(10+x) = 36/(10-x) - 3/2
x = 2

check:

36/12 = 3
36/8 = 4.5
ok

I don't understand the solve.please explain it.

If the current's speed is x, then

10+x is the downstream speed of the boat
10-x is the upstream speed.

the downstream time is 90 minutes (3/2 hours) less than the upstream time. Hence, the given equation.

36/(10+x) = 36/(10-x) - 3/2
36(10-x) = 36(10+x) - 3/2 (10-x)(10+x)
now just expand the factors and collect terms to get

x^2 + 48x - 100 = 0
(x+50)(x-2) = 0

Couldnt get thr ans sir pls solve it..

To determine the speed of the current, we need to set up equations based on the information given.

Let's assume the speed of the current is x kmph.

When the boat is traveling downstream, it benefits from the speed of the current, so its effective speed is increased. We can calculate the downstream speed using the formula:

Downstream Speed = Speed in Still Water + Speed of Current

Therefore, the downstream speed is (10 + x) kmph.

Similarly, when the boat is traveling upstream, it has to work against the current, so its effective speed is reduced. We can calculate the upstream speed using the formula:

Upstream Speed = Speed in Still Water - Speed of Current

Therefore, the upstream speed is (10 - x) kmph.

Now, let's consider the time it takes for the boat to travel downstream and upstream.

The time taken to travel a certain distance is given by the formula:

Time = Distance / Speed

For the downstream journey, the distance is 36 km and the speed is (10 + x) kmph. Therefore, the time taken for the downstream journey is:

Time Downstream = 36 / (10 + x)

For the upstream journey, the distance is still 36 km but the speed is (10 - x) kmph. Therefore, the time taken for the upstream journey is:

Time Upstream = 36 / (10 - x)

According to the given information, the boat takes 90 minutes less time to travel downstream compared to upstream. This is expressed as:

Time Downstream = Time Upstream - 90/60

Substituting the equations we derived for the time taken for each journey, we have:

36 / (10 + x) = 36 / (10 - x) - 90/60

Simplifying this equation allows us to solve for x, the speed of the current.

Let's solve the equation:

36 / (10 + x) = 36 / (10 - x) - 90/60

Simplifying both sides of the equation by multiplying by the denominators, we get:

36(10 - x) = 36(10 + x) - 90(10 + x)

Expanding and simplifying further, we have:

360 - 36x = 360 + 36x - 900 - 90x

Combining like terms:

36x - 36x + 90x = 900 - 360

90x = 540

Dividing both sides by 90:

x = 6

Therefore, the speed of the current is 6 kmph.