Question

In the middle of the park is a giant bucket of water that is attached to a mechanism that is continually losing weight through time. Once the mechanism loses all its weight, the bucket of water pours onto any visitors down below. The amount of weight lost by the mechanism can be expressed as 8x² −2x pounds, where x is the number of hours since loading the contraption. If it originally held 10 pounds, how long will it take for the bucket of water to tip?

a) 2 hours
b) 1 hour
c) 3 hours
d) 4 hours

Answer 1

To determine when the bucket will tip, the quadratic equation 8x² - 2x = 10 is solved for x, yielding x = 1 hour as the time at which the bucket tips.

Step-by-step explanation:

The student is asking for the amount of time it will take for a bucket in a park, which is attached to a mechanism losing weight over time, to tip and pour water. The mechanism loses weight according to the quadratic expression 8x² - 2x pounds, where x is the number of hours since loading the contraption. This weight loss is set against the original weight, which is 10 pounds.

To find out when the bucket will tip, we need to set the quadratic expression equal to the initial weight and solve for x:

8x² - 2x = 10

To solve this quadratic equation, we can first bring all terms to one side to set the equation to zero:

8x² - 2x - 10 = 0

Once we solve for x, we will find the time at which the bucket tips. Solving this, we find that x = 1 hour is the positive solution that makes sense in this context (negative time would not be meaningful).