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Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages ?

Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages ? Correct Answer 8 hours 15 minutes

Number of pages typed by Ronald in 1 hour
$$\eqalign{ & = \frac{{32}}{6} \cr & = \frac{{16}}{3} \cr} $$
Number of pages typed by Elan in 1 hour
$$\eqalign{ & = \frac{{40}}{5} \cr & = 8 \cr} $$
Number of pages typed by both in 1 hour
$$\eqalign{ & = \left( {\frac{{16}}{3} + 8} \right) \cr & = \frac{{40}}{3} \cr} $$
∴Time taken by both to type 110 pages
$$\eqalign{ & {\text{ = }}\left( {100 \times \frac{3}{{40}}} \right){\text{hours}} \cr & = 8\frac{1}{4}{\text{hours}} \cr & = {\text{8 hours 15 minutes}} \cr} $$

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