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A qualified worker digs a well in 5 hours. He invites 2 apprentices, each working \(\frac{3}{4}\) as fast as the qualified worker and 2 trainees each working \(\frac{1}{5}\) as fast as the qualified worker. If the five-person team digs the same well, approximately how much time does the team need to finish the job?

A. 1 hour 24 minutes B. 1 hour 34 minutes C. 1 hour 44 minutes D. 1 hour 54 minutes E. 2 hours 14 minutes

A qualified worker digs a well in 5 hours. He invites 2 apprentices, each working \(\frac{3}{4}\) as fast as the qualified worker and 2 trainees each working \(\frac{1}{5}\) as fast as the qualified worker. If the five-person team digs the same well, approximately how much time does the team need to finish the job?

A. 1 hour 24 minutes B. 1 hour 34 minutes C. 1 hour 44 minutes D. 1 hour 54 minutes E. 2 hours 14 minutes

Follow a basic approach: \(Work=Rate*Time\)

\(Q\) is a rate of a qualified worker.

\(\frac{3}{4}*Q\) - that of an apprentice.

\(\frac{1}{5}*Q\) - that of a trainee.

When people work together, their rates are added. The work is the same, which leads to:

How do we know 1:44 stands for 1 hour 44 mins? I got 50/29 and then just blanked out.... thinking all the answers are in ratios as in 1/24, 1/34 and so on..

Bunuel wrote:

Official Solution:

A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?

A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14

Follow a basic approach: \(Work=Rate*Time\)

\(Q\) is a rate of a qualified worker

\(3\frac{Q}{4}\) - that of an apprentice

\(\frac{Q}{5}\) - that of a trainee

When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\)

A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?

A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14

Follow a basic approach: \(Work=Rate*Time\)

\(Q\) is a rate of a qualified worker

\(3\frac{Q}{4}\) - that of an apprentice

\(\frac{Q}{5}\) - that of a trainee

When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\)

So, \(T=\frac{50}{29}\) or 1:44.

Answer: C

Hi Bunuel,

Would it be wrong to say that Q = 1/5 since it takes 5 hours to do the job?

A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?

A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14

Follow a basic approach: \(Work=Rate*Time\)

\(Q\) is a rate of a qualified worker

\(3\frac{Q}{4}\) - that of an apprentice

\(\frac{Q}{5}\) - that of a trainee

When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\)

So, \(T=\frac{50}{29}\) or 1:44.

Answer: C

Hi Bunuel,

Would it be wrong to say that Q = 1/5 since it takes 5 hours to do the job?

What I did to convert 50/29 was to first get the mix number 1 21/29 => 1 hour and 21/29 minutes.

21/29 is approximately 21/30 ==> 21/29 is approximately 42/60.

Since I increased the denominator by 1 in my estimation, the real value should be bigger. 44 is closest to 42 therefore answer is 1 hour and 44 minutes

A qualified worker digs a well in 5 hours. He invites 2 apprentices, both capable of working \(\frac{3}{4}\) as fast and 2 trainees both working \(\frac{1}{5}\) as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?

A. 1:24 B. 1:34 C. 1:44 D. 1:54 E. 2:14

Follow a basic approach: \(Work=Rate*Time\)

\(Q\) is a rate of a qualified worker

\(3\frac{Q}{4}\) - that of an apprentice

\(\frac{Q}{5}\) - that of a trainee

When people work together, their rates are added. The work is the same, which leads to: \(W = 5Q=(Q+\frac{3}{2}Q+\frac{2}{5}Q)T\) \(5 = \frac{29}{10}T\)

So, \(T=\frac{50}{29}\) or 1:44.

Answer: C

I thought "both capable of working 3/4 as fast..." means that 2 people together work 3/4 as fast as the qualified worker. I think adding to word "each" would be more easier to understand the question.

A qualified worker digs a well in 5 hours. He invites 2 apprentices, each working \(\frac{3}{4}\) as fast as the qualified worker and 2 trainees each working \(\frac{1}{5}\) as fast as the qualified worker. If the five-person team digs the same well, approximately how much time does the team need to finish the job?

A. 1 hour 24 minutes B. 1 hour 34 minutes C. 1 hour 44 minutes D. 1 hour 54 minutes E. 2 hours 14 minutes

I had a slightly different approach. rate for worker - 1/5 time apprentice finishes is 4/3 x5 = 20/3 hours. thus, the rate for 1 apprentice is 3/20. for 2 is 3/10. time of the traine is 5x5=25 hours. rate of 1 trainee 1/25. of 2 trainees = 2/25.

ok, so in 1 hour, they will have: 1/5+3/10+2/25 or 29/50 finished. we thus know for sure that it requires less than 2 hours to finish the job. we are left with 21/50 of the job. we know the rate of all people - 29/50 per hour. thus, the time remaining to finish the job will be: 21/50 x 50/29 = 21/29. multiply this by 60 minutes -> suppose you have 21*60/30 = 21*2 = 42 mins. since denominator was increased, we can think that the mins should be around 42.. only C works.

Rate of the qualified worker - 100/5 - 20 units/hr Rate of the apprentices - 3/4 * 20 - 15 units/hr . Since 2 apprentices , it will be 30 units/hr Rate of the trainees - 1/5 * 15 - 3 units/hr. Since 2 trainees, it will be 6 units/hr

So, the total work done by all of these 5 workers per hour is - 56 units. But the total work is 100 units, so still 45 units of work needs to be done.

60 mins - 56 units. 1 min - 56/60 units - 14/15 units 45 mins - 42 units can be done.

So for approx 1hr 45mins 98 units of work can be done. I'd go with a nearest answer, which would be C.

We are given that a qualified worker digs a well in 5 hours, so if the rate of a qualified worker is Q, then from the formula work = time*rate, we'll get work = 5Q.

efficiency of qualified w=1/5 per hr efficiency of apprentices=1/5 * 3/4 = 3/20 per hr efficiency of trainee=1/5 * 1/5=1/25 per hr total work done in 1 hr 1/5 + 3/20*2 + 1/25 *2 = 29/50 full work will be done in 50/29= 1 hr 44 min ans: c

I'm glad I'm not the only one who saw the hard part as finding 50/29!

Long division takes too long. 50/29 is close to 50/30, which is 5/3. Remember that by making the denominator bigger, the true value of the fraction will be smaller. 5/3 is 1 and 2/3. 2/3 of one hour is 40 minutes. So the estimation is one hour and 40 minutes, with the true value being a little bigger.

B is 1 hour and 34 minutes C is 1 hour and 44 minutes

It's cutting it very close...but for the sake of time answer C is the better answer. I'm not sure of a quicker easier way than this