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.

Guest Nov 24, 2017

#1**+1 **

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

Guest Nov 24, 2017

edited by
Guest
Nov 24, 2017

edited by Guest Nov 24, 2017

edited by Guest Nov 24, 2017

edited by Guest Nov 24, 2017

edited by Guest Nov 24, 2017

edited by Guest Nov 24, 2017

edited by Guest Nov 24, 2017

#2**+1 **

Since Loc can mow the lawn in 20 minutes, his rate is 1 lawn / 20 minutes or 1/20^{th} of the lawn per minute.

Since Reza can mow the lawn in 30 minutes, his rate is 1 lawn / 30 minutes or 1/30^{th} 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)ยท(5) = 5/20^{th} = 1/4^{th} of the lawn.

Now, there is only 3/4^{th} 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

geno3141
Nov 24, 2017

#3**+1 **

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

So

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

CPhill
Nov 25, 2017