Question

A large water bottle has 16.5 fluid ounces of water in it. A smaller water bottle has 8.45 fluid ounces of water in it. The larger bottle is leaking at a rate of 0.15 fluid ounces per hour while the smaller bottle is leaking at a rate of 0.05 fluid ounces per hour. When will there be less water in the larger bottle than there is in the smaller bottle?

A. 5 hours
B. 10 hours
C. 15 hours
D. 20 hours

Answer 1

By setting up equations for the water levels in both bottles over time and solving for when the larger bottle will have less water than the smaller one, it's found that it would take more than 80.5 hours, which does not match any of the provided answer choices. The provided choices may be incorrect.

Step-by-step explanation:

To determine when the larger water bottle will have less water than the smaller bottle, we can set up two equations to represent their water levels over time, taking into account their respective leak rates.

Let t be the number of hours after which we want to find when the larger bottle has less water than the smaller one. For the larger bottle, the amount of water after t hours is:
16.5 - 0.15t (since it loses 0.15 fluid ounces per hour).

For the smaller bottle, the amount of water after t hours is:
8.45 - 0.05t (since it loses 0.05 fluid ounces per hour).

To find out when the larger bottle will have less water than the smaller bottle, we need the following inequality:
16.5 - 0.15t < 8.45 - 0.05t

We solve this inequality for t to find the number of hours it takes for the larger bottle to have less water than the smaller one:

16.5 - 8.45 < 0.15t - 0.05t
8.05 < 0.10t
80.5 < t

Therefore, it would take more than 80.5 hours, so none of the answer choices A through D are correct. There seems to be a mistake in the given answers since none match the calculated value.