22. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream

Let speed x

Speed= D/T
Speed of the boat in upstream= 24/18-x (equation 1)
Speed of boat in down stream= 24/18+x (equation 2)
(Equation 1-2)
24/18-x - 24/18+x= 1
24/18-x= 1+ 24/18+x=18+x+24/x+18=42+x / x+18
28/ x-18= 42+x/x+18

To find the speed of the stream, we need to use the concept of relative speed.

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

When the motorboat is traveling downstream (in the direction of the stream), the speed of the boat with respect to the ground is the sum of its speed in still water and the speed of the stream. So, the speed downstream is (18 + x) km/h.

When the motorboat is traveling upstream (against the direction of the stream), the speed of the boat with respect to the ground is the difference between its speed in still water and the speed of the stream. So, the speed upstream is (18 - x) km/h.

According to the given information, it takes 1 hour more to travel 24 km upstream than the time taken to travel downstream. Let's use the formula for time, distance, and speed to solve this:

Time taken to go downstream = Distance / Speed downstream
Time taken to go upstream = Distance / Speed upstream

Given that it takes 1 hour more to go upstream than downstream, we can write the equation as follows:

24 / (18 + x) = 24 / (18 - x) + 1

Let's solve this equation to find the value of "x":

24 / (18 + x) - 24 / (18 - x) = 1

To simplify this equation, we need to get rid of the denominators by cross-multiplying:

24(18 - x) - 24(18 + x) = (18 + x)(18 - x)

Now let's solve for "x" by simplifying and bringing all the terms to one side:

432 - 24x - 432 - 24x = 324 - x^2

-48x = 324 - x^2

Rearranging the equation:

x^2 - 48x + 324 = 0

Now we'll solve this quadratic equation by factoring or using the quadratic formula. After finding the value of "x," we will have the speed of the stream.