Using Work problem solving , we get
Matilde could take 90 minutes to complete the research project alone .
Raphael could take 3 hr to complete the research project alone.
Work problems are fraction problems :
the following is a simple equation we could use in solving work problems :
1/t₁ + 1/t₂ = 1/td ---> (*)
where,
t₁ = the time it takes for one person to do the work alone
t₂ = the time it takes for the other person to do the work alone
td= the time it takes to do the work when two people are working together.
Now, it is given that matilde twice as long to complete a research project as it takes raphael to do the same research project. They worked together and they could finish similar project in 1 hour.
Let t₁= the time that takes the Raphael working alone
and t₂ = 2t₁= the time it takes for research project working alone
td = times taken by both of researchers to complete the research project together = 1 hr
Now, put the values in above equation (*) we get,
1/t₁ + 1/(2t₁) = 1/1 = 1
Now, we just need to solve for t₁ to get the time it takes for finish the research project work alone.
3/2t₁ = 1 => t₁ = 3/2 hr or 90 minutes
if t₁= 3/2 then t₂ = 2× 3/2 = 3 hr
Hence, matilde will take 3 hr to finish the research project alone and Raphael will take 90 minutes to finish the project work alone.
To learn more about Work problem, refer:
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