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08 Aug 2024, 05:30
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Working at a certain uniform rate, 10 workers take 12 hours to build a solid block 5 meters tall, 6 meters wide, and 12 meters long. How much time will 12 workers take to build a solid block 1 meter taller, 2 meters wider, and 3 meters longer if they work at the same rate?
A) 5 minutes
B) 10 minutes
C) 20 minutes
D) 20 hours
E) 60 hours
A) 5 minutes
B) 10 minutes
C) 20 minutes
D) 20 hours
E) 60 hours
08 Aug 2024, 07:10
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\(\frac{m_{1}\cdot t_{1}\cdot d_{1}}{w_{1}}=\frac{m_{2}\cdot t_{2}\cdot d_{2}}{w_{2}}\)
\(\dfrac{10 \times 12 \text{hr}}{5 \times 6 \times 12 \ m^3} = \dfrac{12 \times x}{1\times 2\times 3 \ m^3}\)
\(x = \dfrac{2}{12} hr = \dfrac{2\times 60}{12} min = 10 \ min\)
B
\(\dfrac{10 \times 12 \text{hr}}{5 \times 6 \times 12 \ m^3} = \dfrac{12 \times x}{1\times 2\times 3 \ m^3}\)
\(x = \dfrac{2}{12} hr = \dfrac{2\times 60}{12} min = 10 \ min\)
B
08 Aug 2024, 08:19
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Volume of first block: \(5 * 6 * 12 = 360 m^3\)
10 workers need 12h for \(360m^3\), that is their hourly rate is \(\frac{360m^3}{12h} = 30 m^3/h\)
Work rate per worker therefor is :\( \frac{30}{10} m^3/h =3m^3/h\)
Volume of second block: \( (5 + 1) * (6 + 2) * (12 + 3) = 720 m^3\)
Given 12 workers with work rate as above, for \(720 m^3\) they need:\(\frac{ 720}{ (12*3)} = 20h\)
IMO: D
10 workers need 12h for \(360m^3\), that is their hourly rate is \(\frac{360m^3}{12h} = 30 m^3/h\)
Work rate per worker therefor is :\( \frac{30}{10} m^3/h =3m^3/h\)
Volume of second block: \( (5 + 1) * (6 + 2) * (12 + 3) = 720 m^3\)
Given 12 workers with work rate as above, for \(720 m^3\) they need:\(\frac{ 720}{ (12*3)} = 20h\)
IMO: D
