SOLUTION: Solve and show all work please. Jane can mow the lawn in 3 hours, and Lester can mow it in 4 hours. If they work together, how long will it take them to mow the lawn?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Solve and show all work please. Jane can mow the lawn in 3 hours, and Lester can mow it in 4 hours. If they work together, how long will it take them to mow the lawn?      Log On


   

Question 37114: Solve and show all work please.
Jane can mow the lawn in 3 hours, and Lester can mow it in 4 hours. If they work together, how long will it take them to mow the lawn?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
if you think about things like this as speed = quantity/time: here the quantity is the lawn area mowed. Lets call this A for area.

So, Jane: Jane's speed = A/3
and Lester: Lester's speed = A/4

together we have still the same Area of lawn in some time, t:
Jane + Lester speed = A/t
+A%2F3+%2B+A%2F4+=+A%2Ft+

all terms have an A, co we can cancel:
+1%2F3+%2B+1%2F4+=+1%2Ft+
+1%2Ft+=+4%2F12+%2B+3%2F12+
+1%2Ft+=+7%2F12+
+t+=+12%2F7+ hours

which is nearly 2 hours. This makes sense --> together it would take an even quicker time.

jon.