Question

Bucket P and Bucket Q are both leaking water. Bucket P contains 750 milliliters of water and is leaking 8 milliliters per minute. Bucket Q contains 800 milliliters of water and is leaking 12 milliliters per minute. Which one of the following equations can you use to find 'm,' the number of minutes it will take for the two buckets to have the same amount of water?

A. 8m + 750 = 12m + 800
B. 800m - 12 = 750m - 8m
C. 750 - 8m = 800 - 12m
D. 12 + 800m = 8 + 750m

Answer 1

To determine the time when both Buckets P and Q will have the same amount of water, we use the equation: 750 - 8m = 800 - 12m. This equates the volumes of water in both buckets as they leak over time.

Step-by-step explanation:

To find 'm', the number of minutes it will take for buckets P and Q to have the same amount of water, we should look for an equation that equates the remaining volumes of water over time as they leak. Starting with the initial volumes of each bucket and subtracting the product of the leak rate and time, we can set up an equation that reflects when both buckets have the same amount of water left.

Bucket P starts with 750 milliliters of water and loses 8 milliliters per minute, so its volume after 'm' minutes is 750 - 8m milliliters. Bucket Q starts with 800 milliliters of water and loses 12 milliliters per minute, thus the volume after 'm' minutes is 800 - 12m milliliters.

To find when they have equal amounts of water, we set these two expressions equal to each other, thus getting the equation: 750 - 8m = 800 - 12m. This is option C and is the correct equation to find 'm'.