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Answer :
Final answer:
To find how long it takes Ahmed to paint the wall by himself, first identify the combined work rate of Jeremy and Ahmed, then subtract Jeremy's individual work rate. Ahmed's work rate is found to be 1/2 wall per hour, which implies it takes him 2 hours to paint the entire wall solo.
Explanation:
The student's question concerns a work rate problem, which is a common topic in algebra and mathematics. To find out how long it would take Ahmed to paint the entire wall by himself, we need to determine the work rate of both Jeremy and Ahmed when they are working together and then subtract Jeremy's individual work rate from their combined work rate to find Ahmed's individual work rate.
Jeremy can paint 1/4 of the wall in 1 hour, so his work rate is 1/4 wall per hour. Together, Jeremy and Ahmed can paint the entire wall in 80 minutes, which is 4/3 hours (since 80 minutes is 4/3 of an hour). This means their combined work rate is 1 wall per 4/3 hours, or 3/4 wall per hour. Now, if we subtract Jeremy's work rate from their combined work rate, we will get Ahmed's work rate:
Combined work rate: 3/4 wall per hour.
Jeremy's work rate: 1/4 wall per hour.
So, Ahmed's work rate is:
3/4 - 1/4 = 2/4 = 1/2 wall per hour.
Finally, if Ahmed can paint 1/2 of the wall in one hour, it would take him 2 hours to paint the entire wall by himself. Hence, the correct answer is (c) 2 hours.
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