Question

A boat whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Answer 1

Ответ:

The speed of the stream is 5km/h

Пошаговое объяснение:

х - speed of the stream

15 + х - speed of the boat downstream

15 - x - speed of the boat contrastream

30/(15 + x) + 30/(15 - x) = 4.5

30(15 - x) + 30(15 + x) = 4.5(15² - x²)

450 - 30x + 450 + 30x = 1012.5 - 4.5x²

4.5 x² = 112.5

x² = 25

x = 5 (km/h)

x = -5 - impossible value

Answer 2

Let's assume the speed of the stream is "x" km/hr.

When the boat is going downstream (i.e., in the direction of the stream), the effective speed of the boat is the sum of its speed in still water and the speed of the stream. So, the effective speed downstream is (15 + x) km/hr.

When the boat is going upstream (i.e., against the stream), the effective speed of the boat is the difference between its speed in still water and the speed of the stream. So, the effective speed upstream is (15 - x) km/hr.

Let's now calculate the time it takes for the boat to go downstream and come back upstream.

Time taken to go downstream = Distance / Speed = 30 km / (15 + x) km/hr Time taken to come back upstream = Distance / Speed = 30 km / (15 - x) km/hr

The total time taken for the whole trip is given as 4 hours and 30 minutes, which is equivalent to 4.5 hours.

So, we can set up the equation:

Time downstream + Time upstream = Total time (30 / (15 + x)) + (30 / (15 - x)) = 4.5

Now, let's solve this equation to find the value of "x" (the speed of the stream):

Multiply everything by (15 + x)(15 - x) to eliminate the denominators:

30(15 - x) + 30(15 + x) = 4.5(15 + x)(15 - x)

Expand and simplify:

450 - 30x + 450 + 30x = 4.5(225 - x^2)

Combine like terms:

900 = 1012.5 - 4.5x^2

Now, isolate the term with x^2:

4.5x^2 = 1012.5 - 900

4.5x^2 = 112.5

Now, solve for x^2:

x^2 = 112.5 / 4.5

x^2 = 25

Finally, take the square root of both sides to find the value of "x":

x = √25

x = 5 km/hr

Therefore, the speed of the stream is 5 km/hr.