Time would be taken by them if they worked together is 1 .875 hours .
What is work and time relationship?
Work is the effort applied to produce a deliverable or accomplish a task. A certain amount of time (T) is taken to complete a certain work (W).
Work Done = Time Taken × Rate of Work.
Rate of Work = 1 / Time Taken.
Time Taken = 1 / Rate of Work.
According to the question
Fred takes 3 hours to dig a garden.
Rate of Work of Fred to dig a garden = 1 / Time Taken.
= 1/ 3
Jason 5 hours to dig a garden.
Rate of Work of Jason to dig a garden = 1 / Time Taken.
= 1/5
Now, Time taken by them if they work together
Work Done = Time Taken × Rate of Work.
Let time taken be t
[tex]\frac{t}{3} + \frac{t}{5} = 1[/tex]
[tex]\frac{8t}{15} = 1[/tex]
t = [tex]\frac{15}{8}[/tex]
t = 1 .875 hours
Hence, Time would be taken by them if they worked together is 1 .875 hours .
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