Answer
The time needed for both Sam and Frank to complete the tour together is $2\frac{1}{10}$ hours.
Work Step by Step
Let $x$ hours be the time for both Sam and Frank to complete the tour together and $W$ be the total work to be done.
Since Sam can complete the tour of the plant in 3 hours, the work to be done by him in 1 hour is $\frac{1}{3}W$,
Same for Frank, since he needs 7 hours to complete the same job, the work to be done by him in 1 hour is $\frac{1}{7}W$,
Now, both Sam and Frank are to perform the work together, the time they needed can be represented as
($\frac{1}{3}W$ + $\frac{1}{7}W$) $\cdot x$ = $W$
($\frac{1}{3}$ + $\frac{1}{7}$) $\cdot x$ = 1
($\frac{7 + 3}{21}$) $\cdot x$ = 1
$x = \frac{21}{10}$
$x = 2\frac{1}{10}$
The time needed for both Sam and Frank to complete the tour together is $2\frac{1}{10}$ hours.
