Question 175440

al, bob, chuck together work at the rate of 1/t truck per hour
al works at the rate of 1/(t+1) truck per hour
bob works at the rate of 1/(t+6) truck per hour
chuck works at the rate of 1/(2t) truck per hour

Now we know that:
(1/(t+1))+(1/(t+6))+(1/(2t))=1/t  multiply each term by 2t(t+1)(t+6)
2t(t+6)+2t(t+1)+(t+1)(t+6)=2(t+1)(t+6) get rid of parens
2t^2+12t+2t^2+2t+t^2+7t+6=2t^2+14t+12 simplify
5t^2+21t+6=2t^2+14t+12  subtract 2t^2, 14t and 12 from each side

3t^2+7t-6=0  quadratic in standard form and it can be factored
(3t-2)(t+3)=0
3t-2=0
t=2/3 hr---------------------------answer
and
t+3=0
t=-3 hrs----disregard--time in this case is positive

CK
1/(2/3 +1) + 1/(2/3+6) + 1/(2*2/3)=1/(2/3)
3/5 + 3/20 + 3/4=3/2
12/20 + 3/20 =15/20=3/2
30/20=3/2
2/2=3/2

Does this help??? ------ptaylor