QuestionFrank can type a report in 7 hours, James in 6 hours. How long for both together?

Studdy Solution

STEP 1

Assumptions1. Frank can type a report in7 hours. . James can type the same report in6 hours.
3. Both Frank and James are working simultaneously on different parts of the report, not on the same part.
4. The speed of typing for both Frank and James remains constant throughout the time they are working.

STEP 2

We need to find the rate at which Frank and James can type. The rate is given by the reciprocal of the time taken.
For Frank, the rate is $Rate_{Frank} = \frac{1}{Time_{Frank}}$

STEP 3

Plug in the given value for the time Frank takes to calculate his rate.
$Rate_{Frank} = \frac{1}{7}$

STEP 4

Similarly, for James, the rate is $Rate_{James} = \frac{1}{Time_{James}}$

STEP 5

Plug in the given value for the time James takes to calculate his rate.
$Rate_{James} = \frac{1}{}$

STEP 6

When Frank and James work together, their rates add up. So, the combined rate is $Rate_{Combined} = Rate_{Frank} + Rate_{James}$

STEP 7

Plug in the values for the rates of Frank and James to calculate the combined rate.
$Rate_{Combined} = \frac{1}{7} + \frac{1}{6}$

STEP 8

Calculate the combined rate.
$Rate_{Combined} = \frac{13}{42}$

STEP 9

The time taken when working together is the reciprocal of the combined rate.
$Time_{Combined} = \frac{}{Rate_{Combined}}$

STEP 10

Plug in the value for the combined rate to calculate the combined time.
$Time_{Combined} = \frac{}{\frac{13}{42}}$

STEP 11

Calculate the combined time.
$Time_{Combined} = \frac{42}{13} \approx3.23 \, hours$ So, it will take approximately3.23 hours for Frank and James to type the report together.

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