Damell is training for a marathon and expects to run at a constant rate for the entire race. If it takes Damell 3 hours to run 15 miles, how long will it take Damell to run 55 miles?

11 hours

Step-by-step explanation:

If Damell is running at a constant rate, we can create a direct proportionality statement, where when one variable (let's call it the mileage, 15 miles) increases, the other also increases (the time, 3 hours). And vice versa.

Written as a direct proportionality statement, let's call it:

time/mileage = time 2.0/mileage 2.0

time = 3

mileage = 15

time 2.0 = x

mileage 2.0 = 55

This would give us something like:

3/15 = x/55 <--- Hey! Fractions!

If we simplify, this is 1/5 = x/55.

Now we should find out how to make both denominators equal (so we have to find the LCM). The LCM of 55 and 5 is 55 (since 5 is a multiple of 55). Therefore, by just multiplying the numerator and denominator of 1/5, we get 11/55.

Now, we have 11/55 = x/55

Since the denominators match, we now know that 11/55 and x/55 are the same fraction. Therefore, the numerators are the same: 11 and x.

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