SOLUTION: Ryan and Eric work for a mail order company. It takes Eric 1 hour longer to fill 100 orders than Ryan. If they work together, it takes them 4hours to fill the orders. Find the amou

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Ryan and Eric work for a mail order company. It takes Eric 1 hour longer to fill 100 orders than Ryan. If they work together, it takes them 4hours to fill the orders. Find the amou      Log On


   

Question 1048457: Ryan and Eric work for a mail order company. It takes Eric 1 hour longer to fill 100 orders than Ryan. If they work together, it takes them 4hours to fill the orders. Find the amount of time required for each individual to fill 100 orders working alone.
Found 2 solutions by jorel555, Boreal:
Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
Let r be the rate at which Ryan works. Then Eric would be r+1. Then you have:
1/r+1/(r+1)=1/4
4(r+1)+4r=rē+r
rē-7r-4=0
Using the quadratic formula; we get r=7.53112887415, or -0.531128874149. Throwing out the negative result, It would take Ryan 7.53112887415 hours and Eric 8.53112887415 hours working alone to fill 100 orders. ☺☺☺☺

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x=number of hours Ryan takes; x+1=number of hours Eric takes
In 1 hour Ryan fills 1/x of the orders
in 1 hour Eric fills 1/(x+1) of the order
Together, it takes them 4 hours
(1/x)+(1/x+1)=(1/4); in 1 hour, they both do 1/4 of the whole project.
multiply through by 4x(x+1)
4(x+1)+4x=(x)(x+1)
4x+4+4x=x^2+x
0=x^2-7x-4
x=(1/2)((7+/-sqrt(65); sqrt (65)=8.06
use positive root.
x=(1/2)(15.06)=7.53 hours for Ryan and 8.53 hours for EricANSWER
in 4 hours, Ryan does 4/7.53 and Eric does 4/8.53, and those are 0.531 and 0.469 with the sum 1.00 of the project.