It takes Maria twice as long to complete a certain type of research project as it takes Judy to do the same project. They both worked on a similar type of project and they finished in 1 hour. How long would each of them take to finish this project working alone? It takes Maria twice as long to complete a certain type of research project as it takes Judy to do the same project. They both worked on a similar type of project and they finished in 1 hour. How long would each of them take to finish this project working alone? It takes Maria twice as long to complete a certain type of research project as it takes Judy to do the same project. They both worked on a similar type of project and they finished in 1 hour. How long would each of them take to finish this project working alone? Solution Let Time taken by Judy to complete the project be \"x\" hour Therefore time taken by Maria to complete the same project be \"2x\" hour Time taken to complete the project if both work together is 1 hour. Workdone by Judy in 1 hour = 1 / x Workdone by Maria in 1hour = 1 / 2x Workdone if they work together in 1 hour = (1/x) + (1/2x) = 2/2x + 1/2x = 3/2x Given that they need 1 hour to complete the task if they work together Therefore Workdone if they work together in 1 hour = 100 % // 100% = 100/100 100/100 = 3/2x 1 = 3/2x 2x = 3 x = 3/2 So Time taken by Judy to complete the project = 3/2 hours Time taken by Maria to complete the project = 2x => 2 * (3/2) => 3 hours.

1. It takes Maria twice as long to complete a certain type of research project as it takes Judy to
do the same project. They both worked on a similar type of project and they finished in 1
hour. How long would each of them take to finish this project working alone?
It takes Maria twice as long to complete a certain type of research project as it takes Judy to
do the same project. They both worked on a similar type of project and they finished in 1
hour. How long would each of them take to finish this project working alone?
It takes Maria twice as long to complete a certain type of research project as it takes Judy to
do the same project. They both worked on a similar type of project and they finished in 1
hour. How long would each of them take to finish this project working alone?
Solution
Let
Time taken by Judy to complete the project be "x" hour
Therefore time taken by Maria to complete the same project be "2x" hour
Time taken to complete the project if both work together is 1 hour.
Workdone by Judy in 1 hour = 1 / x
Workdone by Maria in 1hour = 1 / 2x
Workdone if they work together in 1 hour = (1/x) + (1/2x)
= 2/2x + 1/2x
= 3/2x
Given that they need 1 hour to complete the task if they work together
Therefore Workdone if they work together in 1 hour = 100 % // 100% = 100/100
100/100 = 3/2x
1 = 3/2x
2x = 3

2. x = 3/2
So
Time taken by Judy to complete the project = 3/2 hours
Time taken by Maria to complete the project = 2x => 2 * (3/2) => 3 hours