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11 Dec 2024, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:51) correct
20%
(02:04)
wrong
based on 198
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Larry can hoe a garden in 90 minutes and Jim can hoe it in 60 minutes. They work together for 30 minutes then Jim goes fishing and Larry finishes the job. How much time did Larry spend working alone after Jim left to complete the job?
A) 15 min.
B) 75 min.
C) 42 min.
D) 45 min.
E) 20 min.
A) 15 min.
B) 75 min.
C) 42 min.
D) 45 min.
E) 20 min.
11 Dec 2024, 07:52
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Method 1: Using Efficiency
Find the Total Work (TW), to do so take \(LCM(90, 60) = 180\) (Total Work, TW).
Therefore, efficiency of Larry \(= \dfrac{180}{90} = 2\), and efficiency of Jim \(= \dfrac{180}{60} = 3\)
Remaing amount of work \(= 180 - 150 = 30\). This work is completed by Larry. Hence, the time taken to complete this work is \(\dfrac{30}{2} = 15\) min.
Find the Total Work (TW), to do so take \(LCM(90, 60) = 180\) (Total Work, TW).
Therefore, efficiency of Larry \(= \dfrac{180}{90} = 2\), and efficiency of Jim \(= \dfrac{180}{60} = 3\)
Quote:
Working together for \(30\) min, the amount of work completed, \(30 \times (2+3) = 30 \times 5 = 150\).
Quote:
Remaing amount of work \(= 180 - 150 = 30\). This work is completed by Larry. Hence, the time taken to complete this work is \(\dfrac{30}{2} = 15\) min.
Quote:
ANS A
11 Dec 2024, 23:02
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Larry and Jim worked together for 30 mins, so calculating work done by each in 30 mins -
Larry does 1 job in 90 mins, so in 30 mins he will do \(\frac{1}{3}\) job
Jim does 1 job in 60 mins, so in 30 mins he will do \(\frac{1}{2}\) job
Total work done by both in 30 mins = \(\frac{1}{3}\) + \(\frac{1}{2}\) = \(\frac{5}{6}\)
Jim leaves, work left for Larry = 1 - \(\frac{5}{6}\) = \(\frac{1}{6}\)
We know, Larry does \(\frac{1}{3}\) job in 30 mins, so he will do \(\frac{1}{6}\) job in 15 mins.
A) 15 mins
Larry does 1 job in 90 mins, so in 30 mins he will do \(\frac{1}{3}\) job
Jim does 1 job in 60 mins, so in 30 mins he will do \(\frac{1}{2}\) job
Total work done by both in 30 mins = \(\frac{1}{3}\) + \(\frac{1}{2}\) = \(\frac{5}{6}\)
Jim leaves, work left for Larry = 1 - \(\frac{5}{6}\) = \(\frac{1}{6}\)
We know, Larry does \(\frac{1}{3}\) job in 30 mins, so he will do \(\frac{1}{6}\) job in 15 mins.
A) 15 mins
