the following rational function gives the number of days it would take two construction crews, working together, to frame a house that crew 1 (working alone)could complete in t days and crew 2 (working alone) could complete in t+3 days. f(t)=(t^2+3t)/(2t+3). (a) if crew 1 could frame a certain house in 24 days, how long would it take both crews working together? (b) if crew 2 could frame a certain house in 32 days, how long would it take both crews working together?

Answer 1

It's easier to work with
1/f(t) = 1/t + 1/(t+3)

For crew 1, 1/t = 1/24, so t=24
Thus 1/f(t) = 1/24 + 1/27 = 17/216
So, both crews can do it in 216/17 days

For crew 2, 1/(t+3) = 1/32, so t=29
Now 1/f(t) = 1/29 + 1/32 = 61/928
So, both crews can do it in 928/61 days

Answer 2

Thank you Steve, that was a big help.