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Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
M28-19
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
M28-19
06 May 2023, 03:12
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Official Solution:
Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
After 2 hours, A, working alone, completes \(2*\frac{1}{10}=\frac{1}{5}\) of the task;
After 4 hours, a total of \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task is completed, with A and B working together for the last 2 hours, leaving \(\frac{1}{5}\) of the task remaining;
We know that the final \(\frac{1}{5}\) of the task is completed in 15 minutes (or \(\frac{1}{4}\) of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From this equation, we can determine that \(x=2\) hours.
Answer: C
Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
After 2 hours, A, working alone, completes \(2*\frac{1}{10}=\frac{1}{5}\) of the task;
After 4 hours, a total of \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task is completed, with A and B working together for the last 2 hours, leaving \(\frac{1}{5}\) of the task remaining;
We know that the final \(\frac{1}{5}\) of the task is completed in 15 minutes (or \(\frac{1}{4}\) of an hour) by all three workers: \(\frac{1}{4}*(\frac{1}{10}+\frac{1}{5}+\frac{1}{x})=\frac{1}{5}\). From this equation, we can determine that \(x=2\) hours.
Answer: C
13 Jan 2019, 22:33
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Pick a multiple of 5 and 10 for easy calculation.
Total work can be 50
The efficiency of a = 50/10= 5
The efficiency of a = 50/5=10
The efficiency of a = 50/x
First hour: only a is working- 5 units of work
Second hour: only a is working- 5 units of work
Third hour: a: 5 units of work b: 10 units of work
Fourth hour: a: 5 units of work b: 10 units of work
Total - 40 units of work done, remaining unit- 50-40=10
10/ 5+10+(50/x)= 15/60
ie: Remaing work / efficency of all = time
25x=50
x= 2
Total work can be 50
The efficiency of a = 50/10= 5
The efficiency of a = 50/5=10
The efficiency of a = 50/x
First hour: only a is working- 5 units of work
Second hour: only a is working- 5 units of work
Third hour: a: 5 units of work b: 10 units of work
Fourth hour: a: 5 units of work b: 10 units of work
Total - 40 units of work done, remaining unit- 50-40=10
10/ 5+10+(50/x)= 15/60
ie: Remaing work / efficency of all = time
25x=50
x= 2
General Discussion
13 Jan 2019, 01:37
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A (alone) completes the task in 10 hours, so in 1 hour he does 1/10 of the task
B (alone) completes the task in 5 hours, so in 1 hour he does 1/5 of the task
C (alone) completes the task in x hours, so in 1 hour he does 1/x of the task
A and B combined do : 1/10 + 1/5 = 3/10 of the task in 1 hour hour
A, B and C combined do: 1/10 + 1/5 + 1/x = 3/10 + 1/x of the task in one hour
A starts work and works for 2 hours, so he completes 1/10* 2 = 1/5 of the task
Then A & B work for next 2 hours and complete 3/10*2 = 3/5 of the task
Remaining uncompleted part = 1 - (1/5 + 3/5) = 1/5
This remaining task is done by A, B and C combined in 15 mins.
1/5 = (1/10 + 1/5 + 1/x)*15/60
so x =2
B (alone) completes the task in 5 hours, so in 1 hour he does 1/5 of the task
C (alone) completes the task in x hours, so in 1 hour he does 1/x of the task
A and B combined do : 1/10 + 1/5 = 3/10 of the task in 1 hour hour
A, B and C combined do: 1/10 + 1/5 + 1/x = 3/10 + 1/x of the task in one hour
A starts work and works for 2 hours, so he completes 1/10* 2 = 1/5 of the task
Then A & B work for next 2 hours and complete 3/10*2 = 3/5 of the task
Remaining uncompleted part = 1 - (1/5 + 3/5) = 1/5
This remaining task is done by A, B and C combined in 15 mins.
1/5 = (1/10 + 1/5 + 1/x)*15/60
so x =2
