Question

The Hughes family and the Gonzalez family each used their sprinklers last summer. The Hughes family's sprinkler was used for 15 hours. The Gonzalez family's sprinkler was used for 35 hours. There was a combined total output of 1475 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?

Answer 1

Hughes Family: 40 L/ hour
Gonzalez family: 25L/hour

Explanation:

Let us use the following variables to denote the output rates for each sprinkler.

Let H = water output rate for the Hughes family

Let G = water output rate for the Gonzalez family

(I am using H ang G rather than the traditionally used X and Y to easily identify which rate belongs to which family)

The general equation for the volume of water outputted, V, in time h hours at a rate of r per hour is
V = r x h

Given r

Using this fact
Water Output for Hughes family at rate H for 15 hours = 15H

Water Output for Gonzalez family at rate G for 35 hours = 35 G

The total of both outputs = 1475

That gives us one equation
15H + 35G = 1475 [1]

We are given the combined rate as 65 L per hour
Sum of the two rates = combined rate

H + G = 65 [2]

• Let's write down these two equations and solve for H and G
  15H + 35G = 1475 [1]
  H + G = 65 [2]
  
• Multiply equation [2] by 15 to make the H terms equal
  15H + 15G = 975 [3]
  

• Subtract [3] from [1] to eliminate the H terms
  15H + 35G = 1475
  - - -
  15H + 15G = 975
  --------------------------------------
  0H + 20G = 500
  ---------------------------------------
• So we get
  20G = 500
  G = 500/20 = 25 liters/hour
  
• Plug this value of G into equation [2] to get
  H + 20 = 65
  H = 65 - 25
  H = 40 liters/hour
  
• Water output rates are as follows:
  Hughes Family: 40 L/ hour
  Gonzalez family: 25L/hour