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Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks?
Most Upvoted Answer
Working alone at their respective constant rates, Ajay can complete a ...
Solution:
Step 1: Find their individual rates
Let's assume the job is to paint a room. Ajay can paint the room in 4 hours, so he can paint 1/4 of the room in an hour. Similarly, Firoz can paint 1/3 of the room in an hour.
Step 2: Find their combined rate
When they work together, their combined rate is the sum of their individual rates. So, their combined rate is:
1/4 + 1/3 = 7/12
This means that together, they can paint 7/12 of the room in an hour.
Step 3: Find the total work done
Since they completed the job in 2 hours, we know that the total work done is 1. (Because they completed the whole job.)
Step 4: Find Firoz's work rate
Let's assume Firoz took breaks of length x minutes each time. We know that Ajay worked the whole 2 hours, so he completed the entire job. This means that Firoz also completed the entire job, but he took breaks.
Let's represent Firoz's work rate as r. Then, we know that:
(2/3)r + (x/60)(3/3)r = 1
The first term represents the work Firoz did while working for 2/3 of the time (since he took 3 breaks of equal length). The second term represents the work Firoz did while taking breaks. The (x/60) factor is because we need to convert the break time from minutes to hours to match the units of the work rate.
Simplifying this equation, we get:
(2/3 + x/20)r = 1
Step 5: Solve for x
We can solve for x by rearranging the equation we found in step 4:
x = (20/3)(1 - r)
Step 6: Find Firoz's work rate
We can use the equation we found in step 4 to solve for r:
(2/3 + x/20)r = 1
(2/3 + (20/3)(1 - r)/20)r = 1
(2/3 + (1 - r)/3)r = 1
(2 + 1 - r)r/3 = 1
(3 - r)r/3 = 1
3 - r = 3/r
r^2 - 3r + 3 = 0
Using the quadratic formula, we get:
r = (3 ± √3)i
Since r represents a work rate, it must be positive, so we can ignore the negative solution. Therefore, Firoz's work rate is:
r = (3 + √3)/3
Step 7: Find the length of Firoz's breaks
Finally, we can use the equation we found in step 5 to find the length of F
Community Answer
Working alone at their respective constant rates, Ajay can complete a ...
10 min
if total work was 12 unit
they could do 14unit of work.
out of which ajay would do 6 unitand feroj 8 unit
but feroj did only 6 unit
so he took rest for 25 percent unit of time
which is 30 min
so 10 min each
if total work was 12 unit
they could do 14unit of work.
out of which ajay would do 6 unitand feroj 8 unit
but feroj did only 6 unit
so he took rest for 25 percent unit of time
which is 30 min
so 10 min each
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Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks?
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Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks?.
Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks?.
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Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks?, a detailed solution for Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks? has been provided alongside types of Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz breaks? theory, EduRev gives you an
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