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

Step-by-step 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

$\dfrac{1}{T}=\dfrac{1}{T_1}+\dfrac{1}{T_2}$

$\Rightarrow\ \dfrac{1}{T}=\dfrac{1}{2}+\dfrac13\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{3+2}{2\times3}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{5}{6}\\\\\Rightarrow\ T=\dfrac{6}{5}=1.2$

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