Question

If the answer is 17.5, please explain what happened to 180 and 160. Justin's sand castle is 180 cm tall, but the wind is blowing away sand at a rate of 8 cm per minute. Taylor's sand castle is 160 cm tall, and she is adding sand to it at a rate of 6 cm per minute. After how many minutes will their sand castles be at an equal height?

Options:
1. 10 minutes
2. 20 minutes
3. 30 minutes
4. 40 minutes

Answer 1

By setting up an equation representing the height of Justin's and Taylor's sandcastles over time, we find the castles would be equal in height after approximately 1.43 minutes. However, this does not match any of the provided options, implying there is a mistake in the question.

Step-by-step explanation:

To determine when the sand castles Justin and Taylor are working on will be the same height, we need to figure out the rate at which the height difference between them changes. Justin's sand castle starts at 180 cm and decreases by 8 cm per minute due to wind, while Taylor's starts at 160 cm and increases by 6 cm per minute.

Let's call the minutes passed t. The height of Justin's castle after t minutes will be 180 - 8t (since it decreases), and the height of Taylor's castle will be 160 + 6t (as it increases).

We set these two expressions equal to each other to find out after how many minutes the heights will be equal:
180 - 8t = 160 + 6t

Solving for t, we combine like terms:
14t = 20

Dividing both sides by 14 gives us:
t = 20 / 14t = 10/7t ≈ 1.43 minutes

However, none of the options given (10, 20, 30, 40 minutes) are close to the actual answer. If the selection is supposed to be within these options, there has been an error in the question, as none of the options match the correct computation.