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07 Aug 2026, 10:24
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Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?
(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.
(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.
07 Aug 2026, 10:24
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Official Solution:
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?
Let \(M\) be the number of hours Maya worked, and let \(F\) be the number of hours Felix worked. Nora worked for 2 hours. Since Maya’s shift accounted for 50% of the total time spent on the mural:
\(M = \frac{1}{2} * (M + F + 2)\)
\(M = F + 2\)
Maya painted 25% of the mural, or \(\frac{1}{4}\) of the mural, in \(M\) hours. So Maya’s hourly rate was:
\(\frac{\frac{1}{4}}{M} = \frac{1}{4M}\)
Felix painted 50% of the mural, or \(\frac{1}{2}\) of the mural, in \(F\) hours. So Felix’s hourly rate was:
\(\frac{\frac{1}{2}}{F} = \frac{1}{2F}\)
The question asks how long Maya and Felix would take to paint the entire mural together. So to determine their combined time, we need enough information to determine both \(M\) and \(F\).
(1) Felix worked on the mural for 4 hours.
So \(F = 4\). Since \(M = F + 2\):
\(M = 4 + 2 = 6\)
Now Maya’s and Felix’s rates are fixed, so their combined time is fixed.
Sufficient.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.
This gives:
\(M + 2 = 2F\)
From the stem:
\(M = F + 2\)
So:
\((F + 2) + 2 = 2F\)
\(F = 4\)
Then:
\(M = F + 2 = 6\)
Now Maya’s and Felix’s rates are fixed, so their combined time is fixed.
Sufficient.
Answer: D.
For reference, if \(M = 6\) and \(F = 4\), then Maya’s rate is:
\(\frac{1}{4 * 6} = \frac{1}{24}\)
Felix’s rate is:
\(\frac{1}{2 * 4} = \frac{1}{8}\)
Their combined rate is:
\(\frac{1}{24} + \frac{1}{8} = \frac{1}{24} + \frac{3}{24} = \frac{4}{24} = \frac{1}{6}\)
So together, Maya and Felix would complete the mural in 6 hours.
Answer: D
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?
Let \(M\) be the number of hours Maya worked, and let \(F\) be the number of hours Felix worked. Nora worked for 2 hours. Since Maya’s shift accounted for 50% of the total time spent on the mural:
\(M = \frac{1}{2} * (M + F + 2)\)
\(M = F + 2\)
Maya painted 25% of the mural, or \(\frac{1}{4}\) of the mural, in \(M\) hours. So Maya’s hourly rate was:
\(\frac{\frac{1}{4}}{M} = \frac{1}{4M}\)
Felix painted 50% of the mural, or \(\frac{1}{2}\) of the mural, in \(F\) hours. So Felix’s hourly rate was:
\(\frac{\frac{1}{2}}{F} = \frac{1}{2F}\)
The question asks how long Maya and Felix would take to paint the entire mural together. So to determine their combined time, we need enough information to determine both \(M\) and \(F\).
(1) Felix worked on the mural for 4 hours.
So \(F = 4\). Since \(M = F + 2\):
\(M = 4 + 2 = 6\)
Now Maya’s and Felix’s rates are fixed, so their combined time is fixed.
Sufficient.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.
This gives:
\(M + 2 = 2F\)
From the stem:
\(M = F + 2\)
So:
\((F + 2) + 2 = 2F\)
\(F = 4\)
Then:
\(M = F + 2 = 6\)
Now Maya’s and Felix’s rates are fixed, so their combined time is fixed.
Sufficient.
Answer: D.
For reference, if \(M = 6\) and \(F = 4\), then Maya’s rate is:
\(\frac{1}{4 * 6} = \frac{1}{24}\)
Felix’s rate is:
\(\frac{1}{2 * 4} = \frac{1}{8}\)
Their combined rate is:
\(\frac{1}{24} + \frac{1}{8} = \frac{1}{24} + \frac{3}{24} = \frac{4}{24} = \frac{1}{6}\)
So together, Maya and Felix would complete the mural in 6 hours.
Answer: D
