Question

25. A water tank contains 600 gallons of water and is leaking at a rate of 15 gal/min.
1. Write a linear equation representing the tank volume in terms of time.
II. When will the tank be empty?

a. I. y =- 15x – 600; II. After 40 minutes
b. I. y = 15x – 600; II. After 40 minutes
c. I. y =- 15x + 600; II. After 40 minutes
d. I. y = 15x + 600; II. After 40 minutes

Answer 1

Linear equation is $y = - 15x + 600$ and time is 40 minutes.

Option C is correct.

SOLUTION:

Given that, a water tank contains 600 gallons of water and is leaking at a rate of 15 gal/min.  

We have to find  

1. Required linear equation:  

We know that, remaining tank volume of water = initial volume – lost volume

$\text { Remaining tank volume of water }=600 \text { gallons - speed of leakage } \times \text { time spent} \\\\ \Rightarrow  600-15 \times \text { time }$

Let the remaining volume be y and time spent be x

Then, equation is $y=600-15 x$

2. Period of time when the tank will be empty:  

Tank is empty means y=0 $\rightarrow 600-15 x=0 \rightarrow 15 x=600 \rightarrow x=40$

So, tank will be empty in 40 minutes.