SOLUTION: Rational expressions--Dan & Julio can mow a lawn in 12 minutes. Julio can mow the lawn by himself in 10 minutes less time than it takes Dan by himself. How long does it take each

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Question 31768This question is from textbook elem inter. algebra
: Rational expressions--Dan & Julio can mow a lawn in 12 minutes. Julio can mow the lawn by himself in 10 minutes less time than it takes Dan by himself. How long does it take each of them to mow the lawn alone? This question is from textbook elem inter. algebra

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let Dan's pace be x

let Julio's pace be x-10

Total propotion:

1%2F%28x-10%29%2B1%2Fx=1%2F12

Cross multiply:



2x-10=%28x%5E2-10x%29%2F12

Multiply the whole equation by 12 to remove the fraction:

12%282x%2F1%29-12%2810%2F1%29=12%28%28x%5E2-10x%29%2F12%29

Simplfy:

24x-120=x%5E2-10x

Put it into  form:

x%5E2-34x%2B120=0

Use the quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

In which a=1, b=-34, c=120

x+=+%28-%28-34%29+%2B-+sqrt%28+%28-34%29%5E2-4%2A1%2A120+%29%29%2F%282%2A1%29+ 

Remove the negative sign:

x=%2834%2Bsqrt%281156-480%29%29%2F2

x=%2834%2B26%29%2F2

x=30

30-10=20

Hence, Julio can mow the lawn is 20 minuites and Dan can mow the lawn is 30 minutes when working alone.

Paul.