Question

the Phillips family and the Richardson family each use their sprinklers Last Summer the water output rate for the Philips family sprinkler was 15 L per hour the water output rate for the Richardson family sprinkler was 40 L per hour the family used their sprinklers for a combined total of 50 hours resulting in a water output of 1,250 L how long was each sprinkler used?

Answer 1

Let the Phillips family usage be represented by letter p, and let the Richardson family usage be represented by letter r.

If they used their sprinklers for a total of 50 hours combined, then we can say,

p + r = 50

Also the total water output was 1250 litres. If the Phillips family used theirs at the rate of 15 litres per hour, and the Richardson family used theirs at the rate of 40 litres per hour, we can also express this as,

15p+ 40r = 1250

We now have a system of simultaneous equations which we shall solve as shown below;

`\begin{gathered} p+r=50---(1) \\ 15p+40r=1250---(2) \\ \text{From equation (1), let p = 50-r} \\ \text{Substitute for p = 50-r into equation (2)} \\ 15(50-r)+40r=1250 \\ 750-15r+40r=1250 \\ 750+25r=1250 \\ \text{Subtract 750 from both sides of the equation} \\ 25r=500 \\ \text{Divide both sides by 25} \\ r=20 \\ \text{Substitute for r=20 into equation (1)} \\ p+r=50 \\ p+20=50 \\ \text{Subtract 20 from both sides of the equation} \\ p=30 \end{gathered}`

Where r = 20, and p = 30

Then;

The Phillips' sprinkler worked for 30 hours

The Richardson's sprinkler worked for 20 hours