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Fri Aug 04, 2023 8:00 am
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B
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95% (01:07) correct
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Sharon and Ramla frequently mow their grandfather's yard. Working at her normal pace, Sharon can mow the yard in 5 hours. When Sharon and Ramla work together, each at her own normal pace, they can mow the yard in 3 hours. Yesterday, Ramla mowed the yard by herself. Given that Ramla was mowing at her normal pace, how long, in hours, did it take for Ramla to mow the yard?
A. 7
B. 7.5
C. 8
D. 8.5
E. 9
A. 7
B. 7.5
C. 8
D. 8.5
E. 9
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Sat Aug 12, 2023 5:43 pm
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Sharon and Ramla frequently mow their grandfather's yard.
Working at her normal pace, Sharon can mow the yard in 5 hours.
Since Sharon can mow the yard in 5 hours, her rate is 1/5 yard per hour.
When Sharon and Ramla work together, each at her own normal pace, they can mow the yard in 3 hours.
Since Sharon can and Ramla can mow the yard in 3 hours, their combined rate is 1/3 yard per hour.
Yesterday, Ramla mowed the yard by herself. Given that Ramla was mowing at her normal pace, how long, in hours, did it take for Ramla to mow the yard?
Since their combined rate is 1/3 yard per hour, and Sharon's rate is 1/5 yard per hour, Ramla's rate is 1/3 - 1/5 = 2/15 yard per hour.
So, it took Ramla 15/2 = 7.5 hours to mow the lawn by herself.
The correct answer is (B).
Working at her normal pace, Sharon can mow the yard in 5 hours.
Since Sharon can mow the yard in 5 hours, her rate is 1/5 yard per hour.
When Sharon and Ramla work together, each at her own normal pace, they can mow the yard in 3 hours.
Since Sharon can and Ramla can mow the yard in 3 hours, their combined rate is 1/3 yard per hour.
Yesterday, Ramla mowed the yard by herself. Given that Ramla was mowing at her normal pace, how long, in hours, did it take for Ramla to mow the yard?
Since their combined rate is 1/3 yard per hour, and Sharon's rate is 1/5 yard per hour, Ramla's rate is 1/3 - 1/5 = 2/15 yard per hour.
So, it took Ramla 15/2 = 7.5 hours to mow the lawn by herself.
The correct answer is (B).
General Discussion
Fri Aug 04, 2023 8:23 am
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- Time taken by Sharon to mow the yard \(= t_1 = 5\) hours
- Time taken by Sharon and Ramla to work together to mow the yard \(= t = 3\) hours
- Time taken by Ramla to mow the yard \(= t_2\) hours
Work done together =\(\frac{ t_1 * t_2 }{ t_1 + t_2}\)
\(3 = \frac{5 * t_2}{5+t_2}\)
\(15 + 3t_2 = 5t_2\)
\(2t_2 = 15\)
\(t_2 = 7.5\)
Option B
