Math HW help? Please Explain how its done?

Question

A boat travels 30 miles upstream in 4 hours. The trip downstream takes 2.5 hours. Find the rate of the boat in still water.

Answer 1

Let x = rate of the boat (in still water)

Let y = rate of the stream

Since it is upstream, boat goes against the rate of stream, hence the rate upstream = (x - y)

In downstream, boat's rate and stream's rate are combined, so the rate downstream = (x + y)

Now, distance does not changes and we know that Distance(D) = Rate * Time

Here given boat travels up to stream, D = 30 miles

 30 = 4 (x - y) -->equation(1)

30 = (5/2) (x + y)-->equation(2)

Now, solving both the equations,

4x - 4y = 30-->1

5x + 5y = 60-->2

equation(1) * 5  and equation(2) * 4

20x - 20y = 150-->1

20x + 20y = 240-->2

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40x            = 390

x = 390/40

x = 9.75 mph

we get that the rate of the boat still in water is 9.75mph.