Are you ready to sharpen your skills with work time math problems? This free Work Time Math Problems Quiz is perfect for anyone who wants to conquer time & work quiz challenges and brush up on time and work problems. Test your speed and accuracy, from calculating rates to cracking tricky work and time math questions. Along the way, explore essential questions on time before racing against the clock in our 2 minute math drill. Dive in now, challenge yourself to ace each problem in this time work math quiz, and discover your hidden genius - let the fun begin!
If A can complete a task in 5 hours and B can complete it in 10 hours working alone, how long will it take for them to finish the task working together?
3 hours
3.33 hours
4 hours
2.5 hours
A's rate is 1/5 job per hour and B's rate is 1/10 job per hour. Working together their combined rate is 1/5 + 1/10 = 3/10 job per hour, so time = 1 (3/10) = 10/3 ? 3.33 hours. This uses the formula for combined work rates. Learn more about work rate problems.
If Sam finishes 20% of a job in one hour, how many hours will he take to finish the entire job at the same rate?
4 hours
5 hours
6 hours
8 hours
Completing 20% of a job in 1 hour means Sam's rate is 0.2 job per hour. Time to finish 1 job is 1 0.2 = 5 hours. This applies the rate = work/time relationship. Further reading on rate and work.
If three workers can complete a job in 6 hours, how long would it take two workers at the same individual rate to complete the same job?
4 hours
6 hours
9 hours
12 hours
Three workers finish in 6 hours, so each workers rate is 1/(36)=1/18 job per hour. Two workers combined rate is 2(1/18)=1/9, so time = 1 (1/9) = 9 hours. Rate practice on Khan Academy.
A machine finishes a job in 8 hours. What fraction of the job does it complete in 3 hours?
3/8
1/4
3/5
3/2
The machines rate is 1/8 of the job per hour. In 3 hours it completes 3(1/8)=3/8 of the job. This represents direct proportionality of time and work. Explanation of work fractions.
If a workers production rate is 15 units per hour and the job requires 60 units, how many hours will the worker take?
2 hours
3 hours
4 hours
5 hours
Time = total units rate = 60 units 15 units per hour = 4 hours. This directly follows the formula work = rate time. Review work rate formulas.
If three identical machines each complete 1/6 of a job per hour, how many hours will it take all three working together to finish the job?
1 hour
2 hours
3 hours
4 hours
Each machine does 1/6 per hour, so combined rate = 3(1/6)=1/2 job per hour. Time = 1 (1/2) = 2 hours to finish the job. Worksheets on work rate problems.
If A can do a job in 4 hours and B is twice as fast as A, how long will B take to complete the job alone?
2 hours
3 hours
4 hours
6 hours
As time is 4 hours, so As rate is 1/4 job per hour. B is twice as fast, so Bs rate = 2(1/4)=1/2 job per hour. Time for B = 1 (1/2) = 2 hours. Rate doubling explanation.
If A can do a job in 8 hours and B can do the same job in 12 hours working alone, what fraction of the job do they complete together in one hour?
1/6
5/24
1/4
7/24
As rate is 1/8 and Bs rate is 1/12, so combined rate = 1/8 + 1/12 = (3+2)/24 = 5/24 of the job per hour. Online Math Learning on work rates.
A can complete a job in 6 hours, B in 8 hours, and C in 12 hours. How long will it take them working together?
A and B together can complete a task in 5 hours. A alone takes 8 hours. How long will B alone take to complete the task?
10 hours
13.33 hours
16 hours
20 hours
Combined rate is 1/5. As rate is 1/8. So Bs rate = 1/5 - 1/8 = 3/40, giving Bs time = 40/3 ? 13.33 hours. See a similar problem.
Two inlet pipes fill a tank in 4 hours and 6 hours respectively, while a drain pipe empties it in 12 hours. If all three pipes are open, how long will it take to fill the tank?
2 hours
3 hours
4 hours
6 hours
Inlet rates are 1/4 + 1/6 = 5/12; drain rate is 1/12. Net rate = 5/12 - 1/12 = 4/12 = 1/3. Time = 1 (1/3) = 3 hours. Work and rate problems.
A does 60% of a job in 3 hours, and B finishes the remaining 40% in 4 hours. At this constant rate, how long would B take to complete the entire job alone?
10 hours
8 hours
12 hours
15 hours
Bs rate on the remaining 40% is 0.4 job/4h = 0.1 job per hour. To do 1 job at that rate takes 1 0.1 = 10 hours. CueMath work-rate guide.
Five men can complete a job in 12 days, and three women can complete the same job in 20 days. What is the ratio of one man's daily work rate to one woman's?
1:1
2:3
3:2
4:5
Total work = 5 men12 days = 60 man-days and also = 3 women20 days = 60 woman-days. Thus one man-day equals one woman-day, so individual rates are equal, ratio 1:1. Equal work rates explained.
A and B together finish a job in 6 hours, while B alone takes 8 hours. How long will A take alone?
12 hours
16 hours
24 hours
48 hours
Combined rate = 1/6; Bs rate = 1/8. So As rate = 1/6 - 1/8 = 1/24, giving As time = 24 hours. Rate problem solutions.
A, B, and C working together complete a task in 4 hours; A and B together in 6 hours; B and C together in 12 hours. How long would A alone take to complete the task?
6 hours
8 hours
12 hours
24 hours
Let rates be a, b, c. We have a+b+c=1/4, a+b=1/6. Subtracting gives c=1/12. Also b+c=1/12, so b=0. Then a=1/6, so A takes 6 hours. Work and rates theory.
A does 3/5 of a job in 2 hours. B does the remaining work in 3 hours. At this rate, how long would B take to complete the entire job alone?
6 hours
7.5 hours
9 hours
10 hours
B does 2/5 of the job in 3 hours, so Bs rate = (2/5)/3 = 2/15 job per hour. To do 1 job takes 1 (2/15) = 7.5 hours. Khan Academy: work problems.
A faucet can fill a tank in 6 hours, while a drain can empty it in 8 hours. If both are open, how long will it take to fill the tank?
12 hours
24 hours
4 hours
48 hours
Fill rate is 1/6, empty rate is 1/8. Net rate = 1/6 - 1/8 = (4-3)/24 = 1/24 tank per hour. Time = 1 (1/24) = 24 hours. Net work rate problems.
A and B start a job; after 2 hours, C joins them. If A alone can complete it in 10 hours, B in 15 hours, and C in 30 hours, how long does it take to finish the job from the start?
5.33 hours
6 hours
7 hours
8 hours
A+B rate = 1/10+1/15 = 1/6. In 2h they do 2(1/6)=1/3. Remaining 2/3 done at rate 1/6+1/30=(5+1)/30=1/5, time = (2/3)/(1/5)=10/3?3.33h. Total ?2+3.33=5.33h. Advanced work-rate examples.
A does twice as much work per hour as B. Working together they finish a task in 4 hours. How long will B alone take to complete it?
8 hours
10 hours
12 hours
16 hours
Let Bs rate be r, As is 2r. Together 3r=1/4 ? r=1/12, so Bs time = 12 hours. Rate and work with ratios.
Five men or eight women can complete a job in 12 days. In how many days will three men and four women complete the same job?
9 days
10.91 days
12 days
13.4 days
Total work = 5m12 = 60 man-days and = 8w12 = 96 woman-days. Rate ratio m:w = 96:60 = 8:5. Combined rate of 3m+4w = 31/60+41/96 = 11/120 job per day, so days = 120/11 ? 10.91. Work-rate combinations.
Three pumps A, B, and C can fill a pool in 15, 20, and 30 hours respectively. A and B start filling and after 5 hours C joins. How long in total to fill the pool?
7 hours
7.78 hours
8 hours
8.22 hours
A+B rate = 1/15+1/20=7/60; in 5h they do 35/60=7/12. Remaining 5/12 at rate 1/15+1/20+1/30=3/20, time = (5/12)/(3/20)=25/9?2.78h; total ?5+2.78=7.78h. CueMath pump problems.
A is 20% more efficient than B. Together they finish a job in 5 hours. How long would B take alone to complete it?
A does the first half of a job in 3 hours, and B does the second half in 5 hours. How long would they take working together to complete the entire job?
3 hours
3.75 hours
4 hours
4.25 hours
As rate = (1/2)/3=1/6, Bs rate = (1/2)/5=1/10. Combined rate = 1/6+1/10 = 4/15, so time = 1 (4/15)=15/4=3.75 hours. Purple Math: work rate sums.
Four workers A, B, C, and D take 8, 12, 24, and 48 hours respectively to finish a job alone. They work in rotation one hour each (A then B then C then D, and repeat). How long will it take to complete the job?
14.77 hours
15 hours
16 hours
17 hours
In one 4-hour cycle, work done = 1/8+1/12+1/24+1/48 = 13/48 of the job. Time per cycle is 4 hours, so rate = 13/48 per 4h =13/192 per hour. Time =1(13/192) ?14.77 hours. Complex rotation work problems.
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Study Outcomes
Analyze work rate relationships -
Identify and break down individual and combined work rates to understand how different contributors affect overall task completion.
Apply time and work formulas -
Use standard equations and methods to calculate the time required for single or multiple workers to finish a job.
Solve real-world scenarios -
Work through practical time and work problems that mirror everyday challenges in project planning and resource allocation.
Evaluate task efficiency strategies -
Compare different approaches to completing work faster and identify the most efficient methods for given conditions.
Improve speed and accuracy -
Sharpen calculation skills and reduce errors by practicing rapid problem-solving techniques in our timed time & work math questions quiz.
Track performance growth -
Monitor your quiz scores and analyze errors to set measurable goals for ongoing improvement in work time math problems.
Cheat Sheet
Work Rate Formula -
At the heart of work time math problems is the basic rate formula: Rate (R) = Work (W) ÷ Time (T). For example, if one machine fills a tank in 5 hours, its rate is 1/5 tank per hour. Commit R=W/T to memory - you'll use it in nearly every time & work quiz scenario.
Combined Work Principle -
When two or more workers or machines operate together, you simply add their individual rates to find the combined rate. For instance, if A paints at 1/6 job/hr and B at 1/4 job/hr, together they do (1/6+1/4)=5/12 job per hour. This shortcut from MIT OCW lets you calculate team efficiency in seconds.
Inverse Proportionality Insight -
Time and workforce size are inversely proportional: doubling workers halves the time required. Remember the phrase "More hands, less demands" to recall T ∝ 1/number of workers. This concept, backed by Khan Academy's time and work problems module, is crucial for tricky puzzles.
Time Unit Conversion -
Standardize all units before solving: hours, minutes, days, or seconds must match. For example, 3 days → 3×24=72 hours, and 180 minutes → 3 hours. Flawless conversions ensure accuracy when mixing units in work and time math questions.
Sequential and Fractional Work -
Break complex tasks into fractions completed by different workers or in stages. If Task A completes 40% in 2 hours, the remaining 60% might take longer at a different rate - just apply W_remain ÷ R_new. This stepwise approach, endorsed by university-level problem sets, helps you tackle real-world sequential scenarios.
