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QuestionAdam shovels a driveway in 2 hours, Bev in 3 hours. How long for both to finish together? a) 2:30 b) 2:20 c) 0:48 d) 1:12 e) 1:36

Studdy Solution

STEP 1

Assumptions1. Adam can shovel the driveway in hours. Bev can shovel the same driveway in3 hours3. The time taken by Adam and Bev working together is what we need to find4. The work done by Adam and Bev is additive when they work together

STEP 2

We first need to find the rate at which Adam and Bev can shovel the driveway. The rate of work is defined as the amount of work done per unit time.RateAdam=1TimeAdamRate_{Adam} = \frac{1}{Time_{Adam}}RateBev=1TimeBevRate_{Bev} = \frac{1}{Time_{Bev}}

STEP 3

Now, plug in the given values for the time taken by Adam and Bev to find their rates.
RateAdam=12 hoursRate_{Adam} = \frac{1}{2\, hours}RateBev=13 hoursRate_{Bev} = \frac{1}{3\, hours}

STEP 4

Calculate the rates of Adam and Bev.
RateAdam=0. driveways/hourRate_{Adam} =0.\, driveways/hourRateBev=0.33 driveways/hourRate_{Bev} =0.33\, driveways/hour

STEP 5

Now that we have the rates of Adam and Bev, we can find the combined rate when they work together. The combined rate is simply the sum of their individual rates.
Ratecombined=RateAdam+RateBevRate_{combined} = Rate_{Adam} + Rate_{Bev}

STEP 6

Plug in the values for the rates of Adam and Bev to calculate the combined rate.
Ratecombined=0.5 driveways/hour+0.33 driveways/hourRate_{combined} =0.5\, driveways/hour +0.33\, driveways/hour

STEP 7

Calculate the combined rate.
Ratecombined=0.5 driveways/hour+0.33 driveways/hour=0.83 driveways/hourRate_{combined} =0.5\, driveways/hour +0.33\, driveways/hour =0.83\, driveways/hour

STEP 8

Now that we have the combined rate, we can find the time it would take for Adam and Bev to shovel the driveway together. The time taken is the reciprocal of the rate.
Timecombined=1RatecombinedTime_{combined} = \frac{1}{Rate_{combined}}

STEP 9

Plug in the value for the combined rate to calculate the combined time.
Timecombined=.83 driveways/hourTime_{combined} = \frac{}{.83\, driveways/hour}

STEP 10

Calculate the combined time.
Timecombined=0.83 driveways/hour=.2 hoursTime_{combined} = \frac{}{0.83\, driveways/hour} =.2\, hoursThis is approximately hour and12 minutes. So, the correct answer is (d) hour12 minutes.

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