Working together at their respective constant rates, Bob and Sam can mow a lawn in 12 hoursBob's work rate is \(\frac{1 (job)}{Bob (hours)}\)
Sam's work rate is \(\frac{1 (job)}{Sam (hours)}\)
Their combined work rate is \(\frac{1 (job)}{Bob (hours)} + \frac{1 (job)}{Sam (hours)} = \frac{1 (job)}{12 (hours)}\)
(see:
https://gmatclub.com/forum/combined-rat ... l#p1237427)
Simplify by eliminating units \(\frac{1}{B} + \frac{1}{S}= \frac{1}{12}\)
If Bob’s rate is twice Sam’s rateSo \(\frac{1}{B} = \frac{2}{S}\) (completes two jobs in the time it takes S to complete 1)
New equation
\(\frac{2}{S} + \frac{1}{S} = \frac{1}{12}\)
\(\frac{3}{S}=\frac{1}{12}\)
Cross multiply
S=36
how many hours would it take Bob, working alone, to mow the lawn?\(\frac{1}{B}+\frac{1}{36}=\frac{1}{12}\)
\(\frac{36}{36B} + \frac{B}{36B}=\frac{1}{12}\)
\(\frac{36+B}{36B}=\frac{1}{12}\)
Cross multiply
12(36+B)=36B
36+B=3B
36=2B
18=B
and answer is
B