SOLUTION: can some help me figure this out? Together John, Tina and Chris together completes the yard in 1 hour and 20 minutes. To do it alone John will need twice the time that Tina need

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can some help me figure this out? Together John, Tina and Chris together completes the yard in 1 hour and 20 minutes. To do it alone John will need twice the time that Tina need      Log On


   

Question 77704: can some help me figure this out?
Together John, Tina and Chris together completes the yard in 1 hour and 20 minutes. To do it alone John will need twice the time that Tina needs and two hours more than Chris. how long would it take each to complete the job working alone?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
to find the fraction of the job that each person does, you divide the combined time (80 min) by the individual time---eg. if it takes a group 1 hr to do a job and one of the members can do the job in 2 hr, that person does 1/2 of the job

let x=Tina's time, so 2x=John's time, and 2x-2=Chris' time...together they do the whole job

the equation is %2880%2Fx%29%2B%2880%2F2x%29%2B%2880%2F%282x-2%29%29=1multiplying by 2x(x-1) gives...160x-160+80x-80+80x=2x(x-1)

collecting and rearranging terms gives 2x%5E2-322x%2B240=0 or x%5E2-161x%2B120=0

using quadratic formula: x=%28161+%2B-+sqrt%28161%5E2-4%2A120%29%29%2F2...so x is approx. 160.25 or .75

.75 is less than 80 so NOT possible...so Tina takes 160.25 min...John takes 320.5 min...and Chris takes 200.5 min