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29 Apr 2025, 08:06
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A painter has been hired to paint a wall for 2 dollars per square meter. How much would the painter get for painting the wall?
(1) It will take the painter three hours less to paint the wall at an average rate of 18 square meters per hour than at an average rate of 12 square meters per hour.
(2) It will take the painter 4.5 hours to paint one-fourth of the wall at an average rate of 6 square meters per hour.
(1) It will take the painter three hours less to paint the wall at an average rate of 18 square meters per hour than at an average rate of 12 square meters per hour.
(2) It will take the painter 4.5 hours to paint one-fourth of the wall at an average rate of 6 square meters per hour.
29 Apr 2025, 08:06
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Official Solution:
A painter has been hired to paint a wall for 2 dollars per square meter. How much would the painter get for painting the wall?
Since we are given the price per square meter, we only need to find the area of the wall to get the payment amount.
(1) It will take the painter three hours less to paint the wall at an average rate of 18 square meters per hour than at an average rate of 12 square meters per hour.
Assuming that at the rate of 12 square meters per hour it would take the painter \(t\) hours to paint the wall, we have: \(12t = 18(t-3)\). Solving, we get \(t = 9\). Therefore, the area of the wall is \(12 * 9 = 108\) square meters. Sufficient.
(2) It will take the painter 4.5 hours to paint one-fourth of the wall at an average rate of 6 square meters per hour.
This implies that to paint the whole wall it would take \(4.5 * 4 = 18\) hours. At a rate of 6 square meters per hour, the area of the wall is \(18 * 6 = 108\) square meters. Sufficient.
Answer: D
A painter has been hired to paint a wall for 2 dollars per square meter. How much would the painter get for painting the wall?
Since we are given the price per square meter, we only need to find the area of the wall to get the payment amount.
(1) It will take the painter three hours less to paint the wall at an average rate of 18 square meters per hour than at an average rate of 12 square meters per hour.
Assuming that at the rate of 12 square meters per hour it would take the painter \(t\) hours to paint the wall, we have: \(12t = 18(t-3)\). Solving, we get \(t = 9\). Therefore, the area of the wall is \(12 * 9 = 108\) square meters. Sufficient.
(2) It will take the painter 4.5 hours to paint one-fourth of the wall at an average rate of 6 square meters per hour.
This implies that to paint the whole wall it would take \(4.5 * 4 = 18\) hours. At a rate of 6 square meters per hour, the area of the wall is \(18 * 6 = 108\) square meters. Sufficient.
Answer: D
31 Jul 2025, 11:57
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Hi,I wanted to know that for the second statement we only know the average rate of the painter for painting 1/4th of the wall. For the remaining 3/4 th of the wall, can't his average rate and time be different??
