Concept explainers
To calculate: The time taken by Beth, Bill and Edie to complete the job alone.
Answer to Problem 81AYU
The time taken by Beth is 30 hours, by Bill is 20.03 hours and by Edie is 40 hours to complete the job alone.
Explanation of Solution
Given information:
In 10 hours Beth, Bill and Edie can paint exterior of a home. Bill and Edie can complete the similar task in 15 hours. One fine day all three worked for 4 hours and then Edie left so it took 8 hours to complete the task by Beth and Bill.
Calculation:
Consider the provided information that in 10 hours Beth, Bill and Edie can paint exterior of a home. Bill and Edie can complete the similar task in 15 hours. One fine day all three worked for 4 hours and then Edie left so it took 8 hours to complete the task by Beth and Bill.
Let in one hour the amount of work done by Beth is x, by Bill is y and by Edie is z.
If all three work together and work done in 1 hour is
In 10 hours Beth, Bill and Edie can paint exterior of a home.
So, the equation is
Bill and Edie can complete the similar task in 15 hours.
So, the equation is
One fine day all three worked for 4 hours and then Edie left so it took 8 hours to complete the task by Beth and Bill.
So, the equation is,
So, the system of equation so formed is,
Multiply
Therefore, time taken by Beth is
Multiply
Therefore, time taken by Edie is
Now substitute
Therefore,
Therefore, time taken by Bill is
Thus, the amount placed in treasury bill is
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