Question 876901
Derek's rate is 1/2 car per hour
Allison's rate is 1/5 car per hour
Set t = time to complete
(1/2 + 1/5)t = 1
{{{( (1/2)*(5/5) + (1/5)*(2/2)) t = 1}}}
{{{( (5+2)/10) t = 1}}}
{{{( 7/10) t = 1}}}
multiply each side by 10/7
 {{{t = 1*(10/7)}}}
t = 1 3/7 hours
checking 
(1/2 + 1/5)(10/7) = 1
See 
http://www.wolframalpha.com/input/?i=%281%2F2+%2B+1%2F5%29%2810%2F7%29