Question

A water tank already contained 24 gallons of water before a pump was switched to fill it. The pump started at 10:00 am and by 10:30 am the tank contained 40 gallons of water. By 1:00 pm the tank contained 120 gallons of water. Chapter Reference b Write an equation which will tell the amount of water that the tank containes (W) after the pump was working for T hours.

Answer 1

Answer:

The equation to represent  the amount of water that the tank contains $(W)$ after the pump was working for $T$ hours can be given as:

$W=32T+24$

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 $(W)$ after the pump was working for $T$ 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 = $40-24$ = 16 gallons

Using unitary method:

If in $\frac{1}{2}$ of an hour water filled = 16 gallons

So, in 1 hour the water filled will be = $16\times 2$ = 32 gallons

In 3 hours the water filled will be = $32\times 3$ = 96 gallons

Thus, by 1:00 PM the water in the tank will be = $96+24$ = 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 $(W)$ after the pump was working for $T$ hours can be given as:

$W=32T+24$