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Answer: 24 minutes</h3>
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Explanation:
Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.
Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.
Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.
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Another approach
Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is
1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute
x = number of minutes
(combined rate)*(time) = number of jobs done
(1/24)*x = 1
x = 1*24
x = 24 is the time it takes if they worked together without getting in each other's way.
Effectively, we are solving the equation
1/A + 1/B = 1/C
with
A = time it takes Wilma to do the job on her own
B = time it takes Rocky to do the job on his own
C = time it takes the two working together to get the job done
The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.
So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.
