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Question

Difficulty: EasyInverse Proportions

A maintenance crew uses 44 identical pumps to empty a large aviation fuel tank in 1212 hours. If the crew decides to use 66 of these identical pumps instead, how many hours will it take to completely empty the tank?

Answer: 8 hours

Answer

8 hours
Because the number of pumps and time are inversely proportional, their product must remain constant. The initial scenario gives a product of 4 pumps × 12 hours = 48 pump-hours. To find the new time, divide the constant product of 48 by the new number of pumps (6). 48 ÷ 6 = 8 hours.

Step-by-Step Solution

1
Identify the mathematical relationship between the variables.
The number of pumps and the time required are inversely proportional.
When working at a constant rate, increasing the number of machines decreases the time needed to complete the same job.
2
Set up the inverse proportion equation.
4×12=6×x4 \times 12 = 6 \times x
For inverse proportions, the product of the two variables remains constant (x1y1=x2y2x_1 y_1 = x_2 y_2).
3
Calculate the total pump-hours and solve for the new time.
x=48÷6=8x = 48 \div 6 = 8
Dividing the constant product (48) by the new number of pumps (6) isolates the unknown time variable.

Key Concept

Inverse Proportions
Estimated Time:45s
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Topics

Inverse Proportions

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