SOLUTION: Luke,Eddie, and Ryan can complete a job in 1 hour and 20 minutes if they work together. Working alone, it take Ryan 1 hour more to complete the job than it takes Luke, and Luke wor

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Luke,Eddie, and Ryan can complete a job in 1 hour and 20 minutes if they work together. Working alone, it take Ryan 1 hour more to complete the job than it takes Luke, and Luke wor      Log On


   

Question 605210: Luke,Eddie, and Ryan can complete a job in 1 hour and 20 minutes if they work together. Working alone, it take Ryan 1 hour more to complete the job than it takes Luke, and Luke works twice as fast as Eddie. How much time would it take each to complete the job working alone?
Found 2 solutions by alicealc, richwmiller:
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
Assume there is 1 work,
Luke alone can finish it in L hours,
Eddie alone can finish it in E hours,
Ryan alone can finish it in R hours,
so,
Luke's speed = 1/L
Eddie's speed = 1/E
Ryan's speed = 1/R

Working alone, it take Ryan 1 hour more to complete the job than it takes Luke:
R = 1 + L

Luke works twice as fast as Eddie:
1/L = 2 * 1/E
1/L = 2/E
E = 2L

working together:
1 hour and 20 minutes = 1 20/60 hours = 1 1/3 hours = 4/3 hours
1%2FL+%2B+1%2FE+%2B+1%2FR+=+1%2F%284%2F3%29
1%2FL+%2B+1%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29
2%2F%282L%29+%2B+1%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29
3%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29
%283%2A%281%2BL%29%2B1%2A2L%29%2F%28%282L%29%2A%281%2BL%29%29+=+3%2F4
%283%2B3L%2B2L%29%2F%282L%2B2L%5E2%29+=+3%2F4
%283%2B5L%29%2F%282L%2B2L%5E2%29+=+3%2F4
4%2A%283+%2B+5L%29+=+3%2A%282L%2B2L%5E2%29
12%2B20L+=+6L%2B6L%5E2
0+=+6L%5E2%2B6L-20L-12
0+=+6L%5E2-14L-12
(divide all by 2)
0+=+3L%5E2-7L-6
0 = (3L + 2)*(L - 3)
3L + 2 = 0 or L - 3 = 0
3L = -2 or L = 3
L = -2/3 or L = 3
because the time can't be a negative number, we choose L = 3
R = 1 + L = 1 + 3 = 4
E = 2L = 2 * 3 = 6

so,
Luke alone takes 3 hours to complete the job
Ryan alone takes 4 hours to complete the job
Eddie alone takes 6 hours to complete the job

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Sadly, Alice makes a mistake. She has Eddie working twice as fast as Luke.
Her solution is so nice and neat.
1/L = 2 * 1/E
1/L = 2/E
E = 2L