Loc can mow his entire lawn in 20 minutes; Loc's roommate Reza needs 30 minutes to mow the entire lawn. If Loc starts mowing at 1 p.m., mows for five minutes and then Reza starts to help with his own mower, at what time will they finish mowing the lawn? Express your answer in the form h:mm.
gene3141's answer is correct in the following sense:
Since Loc has already cut 1/4 of the lawn, then there is 3/4 left to cut.
Since Reza takes 30 minutes to cut the whole lawn, it, therefore, will take him: 30 x 3/4=22.5 minutes to cut the remaining 3/4 of the lawn.
1/15 + 1/22.5 =1/9. Take the reciprocal of this:
=9 minutes for both working together to finish the lawn
5 + 9 = 14 minutes after 1 pm, when they will finish
Or 1 + 14 =1:14 pm
Since Loc can mow the lawn in 20 minutes, his rate is 1 lawn / 20 minutes or 1/20th of the lawn per minute.
Since Reza can mow the lawn in 30 minutes, his rate is 1 lawn / 30 minutes or 1/30th of the lawn per minute.
Loc mows for 5 minutes before he his joined by Reza. In these 5 minutes, he can mow (1/20)·(5) = 5/20th = 1/4th of the lawn.
Now, there is only 3/4th of the lawn to finish.
Assuming that the time they mow together is x, we can create this equation:
Amount done by Loc + Amount done by Reza = Total Amount
(1/20)(x) + (1/30)(x) = 3/4
Multiplying both sides by 60:
60(1/20)(x) + 60(1/30)(x) = 60(3/4)
3x + 2x = 45
5x = 45
x = 9 [It will take them 9 minutes, working together, to finish the lawn.]
Adding 9 to the 5 minutes that Loc mows alone = 14 minutes after Loc starts ---> 1:14 pm
Loc mows (1/20) of the lawn in one minute and Reza mows 1/30 of the lawn in one minute....so
in one minute they both mow (1/20 + 1/30) = 50/600 = 1/12 of the lawn
Loc mows (5/20) = 1/4 of the lawn in 5 minutes....so there is 3/4 left to mow
Fraction left to mow / Fraction mowed per minute = additional time required
(3/4) / (1/12) = 36 / 4 = 9 min more......so....the lawn is finished at 1:14