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A paint crew gets a rush order to paint 80 houses in a new d
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20 Dec 2019, 10:39
20 Dec 2019, 10:39
Expert Reply
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Question Stats:
53% (04:03) correct
46% (04:21) wrong based on 32 sessions
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A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
A. \(0.8(80 - y)\)
B. \(0.8 + 0.0025y \)
C. \(\frac{80}{y} —1.25\)
D. \(\frac{80}{1.25y }\)
E. \(80 — 0.25y\)
Kudos for the right answer and explanation
A. \(0.8(80 - y)\)
B. \(0.8 + 0.0025y \)
C. \(\frac{80}{y} —1.25\)
D. \(\frac{80}{1.25y }\)
E. \(80 — 0.25y\)
Kudos for the right answer and explanation
Re: A paint crew gets a rush order to paint 80 houses in a new d
[#permalink]
23 Dec 2019, 10:28
23 Dec 2019, 10:28
2
This may not be the best approach, but here's how I did it.
I assigned values to the variables to start.
Y = 20; X = 4 -- so, the first 20 houses were painted at 4 houses per week.
"Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week."
Rest of the houses = 60 (since we know there are 80 houses, and 20 were painted already). Given the additional support, they will be able to paint these 60 houses at 5 houses per week (1.25x = 1.25(4) = 5, since we assigned x=4).
Combining the pieces of this scenario:
First Y Houses -- 20 houses, at 4/week = 5 Weeks Total
Remaining Houses -- 60 houses at 5/week = 12 Weeks Total
TOTAL WEEKS TO PAINT 80 HOUSES UNDER THIS SCENARIO: 17
If they weren't able to get the additional support, all 80 houses would have been painted at the original rate of 4/week.
80 Houses at 4 Houses / Week = 20 Weeks.
The question asks, "The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?"
To find this, simply set the new scenario total (17 weeks) as the Numerator, and the original scenario (20 weeks) as the denominator. 17/20 = 0.85.
Of course, we're not done -- we need to find out which answer equals 0.85 when you plug in y, which is 20.
A: 0.8(80−y) >> 0.8(60) = 48
B: 0.8+0.0025y >> 0.8 + 0.0025(20) = 0.85 *this is correct!*
C: 80/y - 1.25 >> 80/20 - 1.25 = 2.75
D: 80/1.25y >> 80/1.25(20) = 3.2
E: 80 - 0.25y >> 80 - 0.25(20) = 75
So, may not be the most straightforward way, but for me the easiest way!
PS - I don't think the developers will be happy about the numbers that I chose if that means that it'll take 17 weeks to paint their rush order
I assigned values to the variables to start.
Y = 20; X = 4 -- so, the first 20 houses were painted at 4 houses per week.
"Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week."
Rest of the houses = 60 (since we know there are 80 houses, and 20 were painted already). Given the additional support, they will be able to paint these 60 houses at 5 houses per week (1.25x = 1.25(4) = 5, since we assigned x=4).
Combining the pieces of this scenario:
First Y Houses -- 20 houses, at 4/week = 5 Weeks Total
Remaining Houses -- 60 houses at 5/week = 12 Weeks Total
TOTAL WEEKS TO PAINT 80 HOUSES UNDER THIS SCENARIO: 17
If they weren't able to get the additional support, all 80 houses would have been painted at the original rate of 4/week.
80 Houses at 4 Houses / Week = 20 Weeks.
The question asks, "The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?"
To find this, simply set the new scenario total (17 weeks) as the Numerator, and the original scenario (20 weeks) as the denominator. 17/20 = 0.85.
Of course, we're not done -- we need to find out which answer equals 0.85 when you plug in y, which is 20.
A: 0.8(80−y) >> 0.8(60) = 48
B: 0.8+0.0025y >> 0.8 + 0.0025(20) = 0.85 *this is correct!*
C: 80/y - 1.25 >> 80/20 - 1.25 = 2.75
D: 80/1.25y >> 80/1.25(20) = 3.2
E: 80 - 0.25y >> 80 - 0.25(20) = 75
So, may not be the most straightforward way, but for me the easiest way!
PS - I don't think the developers will be happy about the numbers that I chose if that means that it'll take 17 weeks to paint their rush order
Re: A paint crew gets a rush order to paint 80 houses in a new d
[#permalink]
30 Dec 2019, 08:54
30 Dec 2019, 08:54
1
First scenario would require a time y*(1/x) and the second one y*(1/x)+(1/1.25x )*(80-y). Divide the2nd scenario and the 1st one and you get B) REGARDS!
