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.

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

`W=32t+24`

Explanation:

Let

t ----> the time in hours after 10:00 am (independent variable or x-coordinate)

W ----> the amount of water in gallons that the tank contain (dependent variable or y-coordinate)

Remember that

10:30 am-10:00 am=0.50 hours

1:00 pm-10:00 am=3 hours

we have the ordered pairs

(0.50,40) and (3,120)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(120-40)/(3-0.50)`

`m=(80)/(2.50)`

`m=32(gal)/(h)`

Find the equation in slope intercept form

`W=mt+b`

where

m is the slope

b is the y-intercept

we have

`m=32`

`b=24\ gal` -----> is given (initial value or y-intercept)

`W=32t+24`