Please help with these math problems?

Question

If 4/9 is added to five times the reciprocal of a number, the result is 1. Find the number.

A boat travels 28 miles up the river in the same amount of time it takes to travel 40 miles down the same river. If the current is 3 miles per hour, what is the speed of the boat in still water?

A water faucet can fill a sink in 7 minutes, whereas the drain can empty it in 8 minutes. If the sink is full, how long will it take to empty if both the faucet and the drain are open?

thank you!

Doug · Answer

First problem.
4/9 + 5(1/x) = 1. Subtract 4/9 from both sides

5(1/x) = 5/9. Multiply both sides by x, the number

5 = 5x / 9. Multiply by 9 on both sides.

45 = 5x. Divide by 5 on both sides.

9 = x

? · Answer

4/9+5/x=1

5/x=5/9

x=9

Speed = x

28=(x-3)t      t=28/(x-3)

40=(x+3)t     t=40/(x+3)

28/(x-3)=40/(x+3)
Cross multiply
28(x+3)=40(x-3)
28x+84=40x-120
12x=204
x=17mph

In one minute, the faucet will empty by 1/7-1/8 =1/56
So it will take 56minutes to empty.

Please help with these math problems?

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