Question

apply: rewriting expressions
two pumps are used to empty a water tank. one pump can empty 14 gallons of water per minute, and the second pump can empty 20 gallons per minute.
which expression can be used to determine the change in the number of gallons of water in the tank after m minutes with both pumps working together?
click or tap the correct answer.
a -6m
b -34m
c 6m
d 34m

Explanation:

Step1: Analyze each pump's rate

The first pump empties 14 gallons per minute, so its rate is -14 (negative because it's removing water). The second pump empties 20 gallons per minute, so its rate is -20.

Step2: Find combined rate

To find the total change in gallons after \( m \) minutes, we add the rates of the two pumps and multiply by time \( m \). The combined rate is \( -14 + (-20) = -34 \) gallons per minute. Then, the total change after \( m \) minutes is \( -34 \times m = -34m \).

Answer:

B. -34m