Explore essential concepts of time and work with a focus on efficiency, collaboration, and practical scenarios involving rates of working together, individual productivity, and task completion. Perfect for learners aiming to strengthen their understanding of how combined efforts and efficiency affect job completion times.
If Alex can complete a job in 10 days and Ben can do the same job in 15 days, who is more efficient and why?
Explanation: Alex completes the job in fewer days, making him more efficient, as efficiency in this context refers to doing the same task in less time. Ben is actually less efficient since he takes more time. The option about working more hours is not given in the scenario. The idea of Ben doing less work is incorrect, as they're both doing the same task.
If Worker A can complete a task in 6 hours and Worker B in 12 hours, how long will it take both working together to finish it?
Explanation: Working together, their combined work rate is (1/6 + 1/12) tasks per hour, totaling 1/4. This means the job will take 4 hours. The options of 6, 8, and 9 hours result from incorrect addition or division of individual rates and do not reflect the correct combined efficiency.
If Carla doubles her work efficiency, a task she previously did in 8 days will now take how many days?
Explanation: Doubling efficiency means she works twice as fast, so the time to do the same task is halved: 8 days becomes 4 days. Choosing 6 or 8 days indicates little or no change in efficiency. Sixteen days would be if efficiency was halved, not doubled.
Anna can complete a wall in 5 hours. She works alone for 2 hours, then Jacob joins and they finish in another 1 hour. How long would Jacob take alone to complete the entire wall?
Explanation: Anna completes 2/5 of the wall in 2 hours. Together for 1 hour, they finish the remaining 3/5. Jacob's individual rate thus is the difference needed to finish 3/5 in 1 hour when combined with Anna. Jacob alone would take 15 hours. Options 5 and 7 hours ignore the shared rate; 10 hours results from a miscalculation.
If Sam is twice as efficient as Tom, how many days will they take together to finish a job that Tom alone completes in 12 days?
Explanation: Tom's rate is 1/12, Sam's is 2/12 (since he's twice as fast). Together, their combined rate is 3/12 or 1/4 job per day, so they finish in 4 days. Six, eight, and twelve days don't account for combined efficiency or the doubled rate.
If 4 workers can build a fence in 18 days, how many days would 6 workers take, assuming all work equally?
Explanation: Since the number of workers increases from 4 to 6, the work will be done faster. The total work is the same, so dividing 4 workers by 6 and multiplying by 18 days gives 12 days. The other options are results of incorrect multiplication or division of worker numbers.
Marie can paint a room in 10 hours. If she paints for 4 hours before Tom joins and together they finish in another 2 hours, how long would Tom need to paint the whole room alone?
Explanation: Marie does 4/10 in 4 hours. In the next 2 hours, both do 6/10 together, so Tom’s 2-hour contribution equals 6/10 minus Marie's portion (2/10), which is 4/10. So, Tom alone would take 2 hours for 4/10, making 20 hours for the full room. The distractors arise from misreading the rates or adding/subtracting incorrectly.
If a task is 60% finished by Emma in 3 hours, how long will she need to complete the whole task at the same rate?
Explanation: If 60 percent is finished in 3 hours, then each hour accomplishes 20 percent. Finishing 100 percent would thus take 5 hours. Options 3 and 4 hours are for less than full completion, while 6 hours overestimates the time required.
Sarah and Lucy can complete a project together in 8 days. If Sarah alone can do it in 12 days, how many days would Lucy take to complete it alone?
Explanation: Together their rate is 1/8 per day. Sarah’s rate is 1/12 per day, so Lucy’s rate is 1/8 - 1/12, which is 1/24. Therefore, Lucy would need 24 days alone. The other options are results of incorrect subtraction or inversion of work rates.
Three workers, each completing a job alone in 12, 18, and 36 hours respectively, work together. How many hours do they take to finish the job?
Explanation: Their combined rate per hour is (1/12 + 1/18 + 1/36) = (3+2+1)/36 = 6/36 = 1/6. So, the job will be done in 6 hours. Homes of 8, 9, or 12 hours come from overlooking how individual rates add to increase speed.