High School

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Matt and Morgan are eating cheese poofs. Matt eats 4 poofs per second and Morgan eats 2 poofs per second. Matt gives Morgan a 60-poof head start.

How long will it take Matt to catch up with Morgan? How many cheese poofs will they have eaten?

Answer :

Final answer:

Matt will catch up to Morgan in 30 seconds. At that time, Matt will have eaten 120 cheese poofs, and Morgan will have eaten 180 cheese poofs.

Explanation:

The student is asking about a problem where Matt and Morgan are eating cheese poofs at different rates, and we need to calculate how long it will take Matt to catch up to Morgan, considering Morgan's head start. To do this, we need to use the rates at which they eat and Morgan's head start to find when their total cheese poofs eaten will be equal.

Let t represent the time in seconds for Matt to catch up to Morgan. Matt eats 4 poofs per second, so in t seconds, he will have eaten 4t poofs. Morgan, with a head start of 60 poofs, eats 2 poofs per second, so in t seconds, she will have eaten 2t + 60 poofs. To find out when Matt catches up, we need to set their quantities of eaten poofs equal to each other:

4t = 2t + 60

Solving for t, we get:

4t - 2t = 60

2t = 60

t = 30 seconds

So, it will take Matt 30 seconds to catch up with Morgan. At that time, Matt will have eaten 120 cheese poofs (4 poofs/second × 30 seconds), and Morgan will have eaten 180 cheese poofs (60 poofs head start + 2 poofs/second × 30 seconds).

Learn more about Rate Problem here:

https://brainly.com/question/29624094

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