Question

It normally takes Julius 2 hours to mow the yard, but because he is in a hurry he asks his son, Marcos, to help him. If just his son was doing the yard work it would take him 3 hours. How long will it take if both are working together? Use the formula 1/T_1 +1/T_2 =1/T_both where T_1 is the time required for Julius to complete the job alone, T_2 is the time required for Marcos to complete the job alone, and T_both is the time required to complete the job when they both work together. Answer as a decimal, rounded to one decimal place.

Answer 1

Answer: 1.2 hours

Explanation:

Given: : Time taken by Julius to complete the job alone:
`T_1=2\text{ hours}`

Time taken by Marcos to complete the job alone :
`T_2=3\text{ hours}`

Let the time taken by both to complete the job together = T

`(1)/(T)=(1)/(T_1)+(1)/(T_2)`

`\Rightarrow\ (1)/(T)=(1)/(2)+\frac13\\\\\Rightarrow\ (1)/(T)=(3+2)/(2*3)\\\\\Rightarrow\ (1)/(T)=(5)/(6)\\\\\Rightarrow\ T=(6)/(5)=1.2`

Hence, it will take 1.2 hours to complete the job by working together.