It takes Alexandra 2 hours and 44 minutes to cut the grass. Austin needs 3 hours and 14 minutes to cut the grass. If they work together, how long will it take them to cut the grass?
For problems such as this, it can be handy to remember that .. 1/(1/a +1/b) = ab/(a +b)
The time required to do a job is the inverse of the rate at which the job is done. Rates are added when people work together (in math problems, not in real life).
(2:44)*(3:14)/(2:44 +3:14) = 1:28:52.3
___ 2:44 = 41/15 hours = 82/30 hours 3:14 = 97/30 hours Using the formula above, we have a "working together" time of .. (82/30)*(97/30)/(82/30 +97/30) = 82*97/(30*179) = 3977/2685 . . . hours .. = 1 hour 28 156/179 minutes .. = 1 hour 28 minutes 52 52/179 seconds
___ Learn to use the fraction functions on your calculator. They can be very helpful.
