Tom and Jerry have a mowing business. It takes Tom 30minutes to mow a yard and it takes Jerry 40minutes to mow the same yard. If they worked together, how long will it take them to mow this yard? (Average Rates of Change topic)

Question

lgbasallote · Answer

hintl $$\huge \frac t{30} + \frac t{40} = 1$$
solve for t

lgbasallote · Answer

that would be the answer

anonymous · Answer

How did you get that equation?

anonymous · Answer

I got the answer 120/7 which is correct but how did you come up with that equation? Why does it equal 1?lgbasallote

phi · Answer

I think of these problems as  rate*time = job (almost like rate*time=distance)
rate is measured in job per amount of time
so Tom works at a rate of 1 job/30 mins
Jerry at a rate of 1 job per 40 mins  or 1/40 job/mins
together the rate is  (1/30 + 1/40)
and the equation is
(1/30 + 1/40)*t = 1 job
solve for t (time in minutes)

anonymous · Answer

Wow, that's neat. Thanks :) That makes much more sense.