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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
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#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
#2
+17711
+1

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)ยท(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

geno3141  Nov 24, 2017
#3
+84066
+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

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