Answer:
The equation to represent the amount of water that the tank contains [tex](W)[/tex] after the pump was working for [tex]T[/tex] hours can be given as:
[tex]W=32T+24[/tex]
Step-by-step explanation:
Given:
Water tank initially contained = 24 gallons of water
The pump to fill the tank was switched to fill it.
From 10:00 AM to 10:30 AM the tank contained 40 gallons of water.
By 1:00 PM the tank contained 120 gallons of water.
To write an equation which will tell the amount of water that the tank contains [tex](W)[/tex] after the pump was working for [tex]T[/tex] hours
Solution:
Initially, gallons of water in tank = 24
From 10:00 AM to 10:30 AM the tank had 40 gallons of water.
Thus, in half an hour the pump filled = [tex]40-24[/tex] = 16 gallons
Using unitary method:
If in [tex]\frac{1}{2}[/tex] of an hour water filled = 16 gallons
So, in 1 hour the water filled will be = [tex]16\times 2[/tex] = 32 gallons
In 3 hours the water filled will be = [tex]32\times 3[/tex] = 96 gallons
Thus, by 1:00 PM the water in the tank will be = [tex]96+24[/tex] = 120 gallons
This confirms the data given for 1:00 PM.
This shows that the rate at which the pump fills the tank is 32 gallons of water per hour.
The equation to represent the amount of water that the tank contains [tex](W)[/tex] after the pump was working for [tex]T[/tex] hours can be given as:
[tex]W=32T+24[/tex]
