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15 Mar 2019, 05:34
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Difficulty:
75%
(hard)
Question Stats:
55% (02:20) correct
45%
(02:23)
wrong
based on 181
sessions
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Andy’s lawn has twice as much area as Beth’s lawn and three times as much area as Carlos’ lawn. Carlos’ lawn mower cuts half as fast as Beth’s mower and one third as fast as Andy’s mower. If they all start to mow their lawns at the same time, who will finish first?
(A) Andy
(B) Beth
(C) Carlos
(D) Andy and Carlos tie for first
(E) All three tie
(A) Andy
(B) Beth
(C) Carlos
(D) Andy and Carlos tie for first
(E) All three tie
15 Mar 2019, 07:29
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TyrionLannister
Andy’s lawn has twice as much area as Beth’s lawn and three times as much area as Carlos’ lawn.
Let Andy's lawn = 6 units, Beth's lawn = 3 units, and Carlo's lawn = 2 units.
Carlos’ lawn mower cuts half as fast as Beth’s mower and one third as fast as Andy’s mower.
Let Carlos' rate = 1 unit per hour, Beth's rate = 2 units per hour, and Andy's rate = 3 units per hour.
Since Carlos cuts his 2-unit lawn at a rate of 1 unit per hour, Carlos' time \(= \frac{work}{rate} = \frac{2}{1} = 2\) hours.
Since Beth cuts her 3-unit lawn at a rate of 2 units per hour, Beth's time \(= \frac{work}{rate} = \frac{3}{2} = 1.5\) hours.
Since Andy cuts his 6-unit lawn at a rate of 3 units per hour, Andy's time \(= \frac{work}{rate} = \frac{6}{3} = 2\) hours.
Beth finishes first.
02 Mar 2021, 08:00
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lets assume lawn areas as follows -
c - 100, A - 300, B - 150 (as per the relation given in question)
now per unit mowing time taken by mowers
c - 12, A - 4, B - 6 (as per the relation given in question)
thus total time taken -
c - 1200, A - 1200, B - 900
thus B takes less time.
c - 100, A - 300, B - 150 (as per the relation given in question)
now per unit mowing time taken by mowers
c - 12, A - 4, B - 6 (as per the relation given in question)
thus total time taken -
c - 1200, A - 1200, B - 900
thus B takes less time.
