Question

It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. If they work together, it takes them 3 hours. How many hours would it take Amelie if she worked alone? Round to the nearest tenth

Answer 1

If Amelie worked alone, she would have worked for 4 hours.

We are going to be establishing mathematical relationships to solve this question.

Let t represent the time we are looking for

r to represent Ricardo's rate

a to represent Amelie's rate

we can then say that

1. Ricardo, 1 = r(t + 8)
2. Amelie, 1 = a(t)
3. Together, 1 = (r + a) 3

from the first equation, we can agree that, r = 1/(t+8)

from the second we can also agree that, a = 1/t

If we substitute these two values in the third equation, we have

1 = {1/(t+8) + 1/t} 3, from this we have

t(t + 8) = 3t + 3(t+8)

t² + 8t = 3t + 3t + 24

t² + 8t = 6t + 24, if we collect like terms, we have

t² +8t -6t - 24 = 0

t² +2t -24 = 0,  if we factorize, we have

t² + 6t - 4t - 24 = 0

t(t+6) -4(t+6) = 0

(t+6) (t-4) = 0

t = 4 hours

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