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

Answer:

$W=32t+24$

Step-by-step 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

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{120-40}{3-0.50}$

$m=\frac{80}{2.50}$

$m=32\frac{gal}{h}$

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)

$W=32t+24$