Answer to Question #210258 in Algebra for freebandz

Question

1) A swimming bath can be filled by two pipes,A and B, in 15 hours. If A only is used, it takes 24 hours to fill the bath. How long will it take if B only is used.

2) A liquid X contains 38% alcohol and a liquid Y contains 71% alcohol. In what ratio must X and Y be mixed to obtain a liquid containing 50% alcohol?

Answer 1

1)

Let $x=$ the time taken to fill a swimming bath by pipe B.

Then

$$(\dfrac{1}{24}+\dfrac{1}{x})\cdot15=1$$

$$\dfrac{1}{x}=\dfrac{1}{15}-\dfrac{1}{24}$$

$$\dfrac{1}{x}=\dfrac{1}{40}$$

$$x=40$$

If B only is used, it takes 40 hours to fill the bath. 

2)

Let $x=$ the amount of a liquid X in litres,  $y=$ the amount of a liquid Y in litres.

Then

$$0.38x+0.71y=0.5(x+y)$$

$$0.12x=0.21y$$

$$4x=7y$$

A liquid X and a liquid Y must be mixed in ratio $7\div 4$ to obtain a liquid containing 50% alcohol.