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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sat Jul 16, 2011 7:50 pm

It takes 7 high school kids, working at the same constant rates, 10 hours to paint a certain house. At what time will the house be complete if 7 kids start painting at 9am and one kid (assume identical rates for all kids) is added per hour starting 1 pm?

A. 3 pm
B. 4:30 pm
C. 5 pm
D. 5:20 pm
E. 6:20 pm

my answer is not D and here is what i did ... can you guys please help me where i made it wrong,ok?
7 kids paint a house in 10 hours so 1 kids will paint a house in 70 hours so 8 kids will paint a house in 70/8=8.75 hours
from 9 am till 1 pm is totally 4 hours and for 4 hours 7 kids painted 2/5 house so there would be 3/5 house left
so 8 kids will paint 3/5 house in =8.75*3/5=5.25 hours....
where did i do wrong?

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Source: Beat The GMAT — Problem Solving | Sat Jul 16, 2011 7:50 pm

winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Sat Jul 16, 2011 9:01 pm

Hi,
You haven't really understood the question well..
At 1 PM and onwards after each hour there will be an addition of 1 kid after EACH hour.
so 7 kids take 70 hours, total work needed = 70 hrs.
at 1 PM = 28 hrs
at 2 pm= + 8 hrs
at 3 pm= + 9 hrs
at 4 pm= + 10hrs
at 5 pm= + 11hrs(At this point you reach 66 hrs, you need 4 hrs to complete 70 hrs and there are now 12 kids so 4/12)
at 5:20= + 4 hrs
Total= 70Hrs

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mirantdon: Master | Next Rank: 500 Posts; Posts: 135; Joined: Thu May 05, 2011 9:00 amFollowed by: 1 member; Thanked: 4 times; GMAT Score:700

by mirantdon » Sun Jul 17, 2011 2:29 am

Good question +1 for D.
I did it the other way .
4/10 of the work is done by 1 pm
The remaining work = 0.6 .
So after 1 pm = (1/10 +1/70)[ work done by 7 of them plus the additional guy(1/70)]
2 pm = (1/10 +2/70)

Keep adding values till you reach 0.6 .. Use the options as well . they are pretty far apart .!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 17, 2011 4:00 am

diebeatsthegmat wrote:It takes 7 high school kids, working at the same constant rates, 10 hours to paint a certain house. At what time will the house be complete if 7 kids start painting at 9am and one kid (assume identical rates for all kids) is added per hour starting 1 pm?

A. 3 pm
B. 4:30 pm
C. 5 pm
D. 5:20 pm
E. 6:20 pm

my answer is not D and here is what i did ... can you guys please help me where i made it wrong,ok?
7 kids paint a house in 10 hours so 1 kids will paint a house in 70 hours so 8 kids will paint a house in 70/8=8.75 hours
from 9 am till 1 pm is totally 4 hours and for 4 hours 7 kids painted 2/5 house so there would be 3/5 house left
so 8 kids will paint 3/5 house in =8.75*3/5=5.25 hours....
where did i do wrong?

Let rate per kid = 1 unit per hour.
Rate of 7 kids = 7 units per hour.
Work completed over 10 hours = r*t = 7*10 = 70 units.
Work completed by 7 kids from 9am to 1pm = 7*4 = 28 units.
Remaining work = 70-28 = 42 units.
Since each kid produces 1 unit per hour, as a kid is added each hour, the amount of work produced increases by 1 unit.
Over the next 4 hours, work produced = 8+9+10+11 = 38 units.
Time is now 1pm + 4 hours = 5pm.
Remaining work = 42-38 = 4 units.
Since only 4 more units need to be produced, the work is completed between 5pm and 6pm.

The correct answer is D.

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goalevan: Master | Next Rank: 500 Posts; Posts: 111; Joined: Tue Dec 30, 2008 1:25 pm; Location: USA; Thanked: 28 times; GMAT Score:770

by goalevan » Sun Jul 17, 2011 7:11 am

Rate 7 kids = work/time = 1 house / 10 hours = 1/10 house/hour
Rate of 1 kid (each kid works at an equal rate) = 1/10 * 1/7 = 1/70 house/hour

For the first 4 hours, 9am - 12:59pm:
7 kids * 1/70 house/hour * 4 hours = 28/70 houses

New time: 1:00pm. Remaining work: 42/70 houses

For the next hours, 1:00-4:59pm:
8 kids * 1/70 house/hour * 1 hour = 8/70 houses
9 kids * 1/70 house/hour * 1 hour = 9/70 houses
10 kids * 1/70 house/hour * 1 hour = 10/70 houses
11 kids * 1/70 house/hour * 1 hour = 11/70 houses

New time: 4:00pm. Remaining work: 4/70 houses

12 kids * 1/70 house/hour * x hours = 4/70 houses
x = (4/70) / (12/70) = 4/12 = 1/3 hours.

Cumulative time is 4 + 1 + 1 + 1 + 1 + 1/3 hours or 8hrs:20min.

9:00am + 8hrs:20min = 5:20pm. D

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sun Jul 17, 2011 9:10 am

winniethepooh wrote:Hi,
You haven't really understood the question well..
At 1 PM and onwards after each hour there will be an addition of 1 kid after EACH hour.
so 7 kids take 70 hours, total work needed = 70 hrs.
at 1 PM = 28 hrs
at 2 pm= + 8 hrs
at 3 pm= + 9 hrs
at 4 pm= + 10hrs
at 5 pm= + 11hrs(At this point you reach 66 hrs, you need 4 hrs to complete 70 hrs and there are now 12 kids so 4/12)
at 5:20= + 4 hrs
Total= 70Hrs

ohh yeah i forgot reading the word "per hour". My bad!

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Mon Jul 18, 2011 10:05 pm

total man hours = 7*10 = 70

till 1 pm man hours = 7*4 = 28

till 5 pm man hours = 28 + 8 + 9 + 10 + 11 = 66

till 6 pm man hours = 66+12 = 78.

thus D is perfect.

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