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.

step-by-step explanation:

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584