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WORK PROBLEMSWorking TogetherWORK PROBLEMSKEY CONCEPTS: Time to complete job alone VS Work rate Work Rate x Time Worked = Fraction of job done

BIG IDEA: Different Contributions add up to complete ONE jobWork rate is the rate at which a task can be doneExample: If a painter can paint a room in 8 hours, then the task is to paint the room.

In other words, the painter can complete 1/8 of the task per hour. If he works for less than 8 hours, then he will perform a fraction of the task. For example,

4If a painter can paint a room in 8 hours and an apprentice painter can paint the same room by himself in 10 hours, how long will it take them to paint the house together?

Then we say that he can complete 1/10 of the task per hour. Let t represent the time it takes both of the painters, working together, to paint the room.

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In general, we have the following work-rate formula:

Here 1 and 1 are the individual work t1 t2 rates and t is the time it takes to complete one task working together.

8 If we factor out the time, t, and then divide both sides by t, we obtain an equivalent work-rate formula:

2. Working alone, Billys dad can complete the yard work in 3 hours. If Billy helps his dad, then the yard work takes 2 hours. How long would it take Billy working alone to complete the yard work?

The amount of the task each completes will total 1 completed task.

To solve for x, we first multiply both sides by the LCD, 3x13Joes garden hose fills the pool in 12 hours. His neighbor has a thinner hose that fills the pool in 15 hours. How long will it take to fill the pool using both hoses?Video Solution

Grace can do a job in 3 hours while John needs 5 hours to finish the same job. How long will it take them if they work together?

WorkRateTimeWork doneGrace

John

TRY THISSuppose a swimming pool has two intake pipes. One pipe fills the pool in 10 hours and the other in 15 hours. If both pipes are open, how long will it take to fill the pool?WorkRateTimeWork done1st pipe

2nd pipe

Let x = the number of hours it takes for both pipes to fill the pool

1/10 + 1/15 = 1/xX = 6 hrs184. Working together, two construction crews can build a shed in 5 days. Working separately, the less experienced crew takes twice as long to build a shed than the more experienced crew. Working separately, how long does it take each crew to build a shed?

Let x represent the time it takes the more experienced crew to build a shed.Let 2x represent the time it takes the less experienced crew to build a shed.Working together, the job is completed in 5 days. This gives the following setup:

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To determine the time it takes the less experienced crew, we use 2x:

Answer: Working separately, the experienced crew takes 7 days to build a shed, and the less experienced crew takes 15 days to build a shed

AloneRateTimeWork doneExperienced bricklayer

Apprentice

An experienced landscaper can landscape a lawn in 36 hours. A not so experienced landscaper can do the job in 45 hours. How long would it take them to landscape the lawn if they work together?

Machine A can do a job in 10 hours, Machine B can do a job in 15 hours and Machine C can do it in 20 hours. If all three machines were used at the same time, how long would it take to finish the job?

An experienced bricklayer can work twice as fast as an apprentice bricklayer. If it takes the two bricklayers 8 hours to finish the job, how long would it take each to do the job alone?

Two guys are working on your car. The first guy can complete the given job in six hours while the second guy needs eight hours. They worked together for two hours, but the first guy left to help another mechanic on a different job. How long will it take the second guy to finish the job?

EXERCISES!!!A bathtub can be filled with water in 20 minutes while the drain can empty it in 30 minutes. How long will it take to fill the bathtub if both the faucet is on and the drain is open?

One pipe can fill a pool 5/4 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?

A bathtub can be filled with water in 20 minutes while the drain can empty it in 30 minutes. How long will it take to fill the bathtub if both the faucet is on and the drain is open?

Two guys are working on your car. The first guy can complete the given job in six hours while the second guy needs eight hours. They worked together for two hours, but the first guy left to help another mechanic on a different job. How long will it take the second guy to finish the job?

Working alone, Emeline can complete the job in 100 min. while Analyn can complete the same task in two hours. They already worked together for 30 min when their sister Len, helped them and finished the task 20 minutes later. How long would it take Len to finish the job alone?