nikhilgmat31 wrote:It takes 7 high school students, working at identical constant individual rates,
10 hours to paint a certain house. At what time will the house be fully painted
if 7 students start painting at 9AM and one student, working at the same rate,
is added per hour starting at 1PM?
(A) 3:00PM
(B) 4:30PM
(C) 5:00PM
(D) 5:20PM
(E) 6:20PM
Let the rate per student = 1 unit per hour.
Rate for 7 students = 7 units per hour.
Since 7 students can paint the house in 10 hours, the house = rt = 7*10 = 70 units.
9am-1pm: 7 students
Amount of work produced by 7 students in these 4 hours = rt = 7*4 = 28 units.
Remaining work = 70-28 = 42 units.
1pm-2pm: 8 students
Amount of work produced = 8 units.
Remaining work = 42-8 = 34 units.
2pm-3pm: 9 students
Amount of work produced = 9 units.
Remaining work = 34-9 = 25 units.
3pm-4pm: 10 students
Amount of work produced = 10 units.
Remaining work = 25-10 = 15 units.
4pm-5pm: 11 students
Amount of work produced = 11 units.
Remaining work = 15-11 = 4 units.
Since only 4 units remain, it will take less than 1 more hour for the rest of house to be painted.
The correct answer is
D.
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