QuestionJackie takes 5 hours and Lisa takes 6 hours to paint. How long to paint together? Give the answer as a reduced fraction.
Studdy Solution
STEP 1
Assumptions1. Jackie can paint the room in5 hours. Lisa can paint the room in6 hours3. Both Jackie and Lisa work at a constant rate4. The work done by Jackie and Lisa is additive when they work together
STEP 2
First, we need to find the rate at which Jackie and Lisa can paint the room. The rate is the reciprocal of the time it takes to complete the task.
STEP 3
When Jackie and Lisa work together, their rates add up. So, the combined rate is the sum of their individual rates.
STEP 4
Substitute the values of and into the equation.
STEP 5
To add these fractions, we need a common denominator. The least common multiple of5 and is30.
STEP 6
Add the fractions to find the combined rate.
STEP 7
The time it takes for them to paint the room together is the reciprocal of their combined rate.
STEP 8
Substitute the value of into the equation.
STEP 9
Calculate the time it takes for them to paint the room together.
So, it would take Jackie and Lisa hours to paint the room together.
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