Does it ask for 1/(w1+w2+ w3+ w4+ w5) or 1/w1+1/w2+1/w3+1/w4+1/w5 ?HallsofIvy said:Yes, that's exactly right. When people work together, their rates add. If W1 can do a job in w1 hours, he/she works at a rate of 1/w1 "job per hour".
So
"Each one of the five workers W1, W2, W3, W4 and W5 can do a certain job.
W1, W2, W3 together can do it in 7.5 hours." 1/w1+ 1/w2+ 1/w3= 1/7.5
"W1, W3, W5 together can do it in 5 hours." 1/w1+ 1/w3+ 1/w5= 1/5
"W1, W3, W4 together can do it in 6 hours." 1/w1+ 1/w3+ 1/w4= 1/6
"W2, W4, W5 together can do it in 5 hours." 1/w2+ 1/w4+ 1/w5= 1/5
Since you have only four equations in five unknowns, you cannot solve for the five values separately. Fortunately, the problem does not ask you to. It asks for 1/(w1+w2+ w3+ w4+ w5).
You're right, almost. Halls confused himself at the final step. You need 1/(1/w1+1/w2+1/w3+1/w4+1/w5).agoogler said:Does it ask for 1/(w1+w2+ w3+ w4+ w5) or 1/w1+1/w2+1/w3+1/w4+1/w5 ?
The reciprocal of the total rate should be the time required . Um , since the first condition says r1+r2+r3=1/7.5 , I think I only need to find r4 and r5 then add it to that. Right ?haruspex said:You're right, almost. Halls confused himself at the final step. You need 1/(1/w1+1/w2+1/w3+1/w4+1/w5).
It would be easier to think about working in terms of rates, r1..r5, rather than these inverted rates. But the equations are essentially the same: r1+r2+r3 = 1/7.5 etc. All working together, the total rate is r1+r2+r3+r4+r5. How do you turn that into the time they'll take?
Btw, there's something a bit special about the provided information which allows you to get the answer without finding all of r1 to r5. Can you see what it is?
I do that a lot!haruspex said:You're right, almost. Halls confused himself at the final step.
You need 1/(1/w1+1/w2+1/w3+1/w4+1/w5).
It would be easier to think about working in terms of rates, r1..r5, rather than these inverted rates. But the equations are essentially the same: r1+r2+r3 = 1/7.5 etc. All working together, the total rate is r1+r2+r3+r4+r5. How do you turn that into the time they'll take?
Btw, there's something a bit special about the provided information which allows you to get the answer without finding all of r1 to r5. Can you see what it is?
Yes. (The special fact about the given data is that W1 and W3 always occur together, so as far as the sum of all five is concerned they constitute only one unknown.)agoogler said:The reciprocal of the total rate should be the time required . Um , since the first condition says r1+r2+r3=1/7.5 , I think I only need to find r4 and r5 then add it to that. Right ?
So I just tried to solve it and got the answer 10/3 , Am I right?haruspex said:Yes. (The special fact about the given data is that W1 and W3 always occur together, so as far as the sum of all five is concerned they constitute only one unknown.)
agoogler said:So I just tried to solve it and got the answer 10/3 , Am I right?
LOL , I didn't notice that. Thanks !haruspex said:Yes. Fwiw, the easiest way is to take all the equations like r1+r2+r3=1/7.5, add them up, and add the last one (r2, r4, r5) in again. On the LHS you then have 3(r1+r2+r3+r4+r5).
A word problem about finding the time in which workers can do a job is a mathematical scenario that involves determining the amount of time it takes for a specific number of workers to complete a task.
To solve a word problem about finding the time in which workers can do a job, you need to identify the given information such as the number of workers, the amount of work to be done, and the rate at which the workers can complete the job. Then, you can use the formula time = (amount of work) / (rate of work) to calculate the time it takes for the workers to finish the job.
The time it takes for workers to complete a job can be affected by various factors such as the number of workers, their individual skills and efficiency, the complexity of the task, the availability of resources, and any potential obstacles or interruptions.
To determine the most efficient way for workers to complete a job, you can consider factors such as the number of workers needed, their skills and abilities, the division of tasks, and any potential obstacles. You can also use mathematical calculations and analysis to optimize the time and effort required for the workers to finish the job.
It is important to accurately calculate the time it takes for workers to complete a job because it allows for better planning and scheduling of tasks, efficient use of resources, and meeting project deadlines. It also helps in evaluating the productivity and performance of workers and identifying areas for improvement.