Nathan can unload one truck in 4 hours. Iris can unload one truck in 6 hours.

Let's say they are both working on separate trucks. After 4 hours, Nathan will finish unloading his truck. Iris will have \(\frac{4}{6}\) of her truck unloaded. Now Nathan comes and join Iris to help her finish unloading her truck.

Clearly, it's going to take them longer than 4 hours to get both trucks unloaded. So we can eliminate choices C, D, and E right off the bat.

If we give them another hour, though, Iris will contribute another \(\frac{1}{6}\) of the truck, and Nathan will contribute another \(\frac{1}{4}\). But since \(\frac{1}{4}\) is greater than \(\frac{1}{6}\), together they'll contribute more than the \(\frac{2}{6}\) still remaining to unload off of Iris's truck. In other words, 5 hours is too long. The answer must be B.

Alternatively, Nathan can unload \(\frac{1}{4}\) of a truck per hour. Iris can unload \(\frac{1}{6}\) of a truck per hour. Together, then, they can unload \(\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}\) of a truck per hour.

So if they can unload \(\frac{5}{12}\) of a truck per hour, how many hours will it take them to unload \(\frac{24}{12}\) of a truck (that is, 2 trucks)?




What is 24/12...How it Came?

Algebraically:

\(\frac{5}{12}x = \frac{24}{12}\)

\(x = \frac{24}{12} \times \frac{12}{5} = \frac{24}{5} = 4.8\)

So it will take them 4.8 hours to unload 2 trucks. Only B is between 4 and 5 hours.