Question

Pam, Sam and Tam working together can complete a job in $8$hours. Pam alone can finish the job in $20$hours, and Sam alone in $24$hours. How long will Tam, working alone, take to finish the job on his own?

Answer 1

Hint: The given problem can be converted into the division of the given values like eight hours can be converted into$\dfrac{1}{8}$.
So that we can make use of the division operator and try to find the unknown values by simplification in the division terms.

Complete step-by-step solution:
First, convert every given thing according to the division.
Starting with the person Pam alone who is able to finish the given work in twenty hours with no one helped can be converted into$P = \dfrac{1}{{20}}$.
Second, the person Sam alone is able to do the same work that Sam did, which is required twenty-four hours (more than Sam working hours) can be converted into$S = \dfrac{1}{{24}}$.
For the Tam, there are no given working hours and we have to find that so make the variable x for the simplification purpose, thus we get the converted hours is$T = \dfrac{1}{x}$.
Also, given that Pam, Sam, and Tam all of them working together can complete a job in eight hours, thus converted into $P + S + T = \dfrac{1}{8}$(all three working hours).
Hence, we know the values for Pam and Sam, substituting the values we get \[P + S + T = \dfrac{1}{8} \Rightarrow \dfrac{1}{{20}} + \dfrac{1}{{24}} + \dfrac{1}{x} = \dfrac{1}{8}\]since we need to find the working hours for the Tam only.
So, make the value x on the left side and all other values on the right side we get\[ \Rightarrow \dfrac{1}{x} = \dfrac{1}{8} - \dfrac{1}{{20}} - \dfrac{1}{{24}}\].
Cross multiplied with the use of the LCM method we get\[ \Rightarrow \dfrac{1}{x} = \dfrac{{15 - 6 - 5}}{{120}} = \dfrac{1}{{30}}\].
Now convert the value x in the numerator we get, $x = 30$ which is the required hours for Tam to complete the work alone.

Note: We cannot solve this problem without converting the terms into division terms, if we do that the answer is wrong.
There are many other problems like finding the missing working hours, finding the working days we have to convert and solve these kinds of problems.
LCM is the method of Least common multiple, where find the least numbers from the common multiples of two or more than two numbers.