ACT Math · Ratios, rates, and percents
A painter can paint a room alone at a rate of 1/5 of the room per hour. After working alone for 2 hours, a second painter joins, and…
A painter can paint a room alone at a rate of of the room per hour. After working alone for 2 hours, a second painter joins, and together they finish painting the remaining part of the room in 1.5 hours. What is the second painter's rate, in rooms per hour, working alone?
Answer and explanation
Answer: C: 1/5
After 2 hours, the first painter has completed 2(1/5)=2/5 of the room, leaving 3/5 remaining. Working together, they complete this remaining 3/5 in 1.5 hours, so their combined rate is (3/5)/1.5 = 2/5 rooms per hour. Since the first painter's individual rate is 1/5, the second painter's rate alone is 2/5 − 1/5 = 1/5. Choice D reports the combined rate instead of isolating the second painter's individual contribution.
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