Bunuel wrote:

Kathleen can paint a room in 3 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?

A. 8/15

B. 4/3

C. 15/8

D. 9/4

E. 15/4

It is always useful to assume the total work units in such questions. This makes the calculations easier.

Always assume the total work units as the LCM of the time taken.

Assume total work units = 15 units.

Kathleen can paint at \(\frac{15}{3}\) = 5 units/hour

Anthony can paint at \(\frac{15}{5}\) = 3 units per hour.

Together they will paint 15 units in \(\frac{15}{{3 + 5}}\) = \(\frac{15}{8}\) hours.

Hence time required to pain two such rooms = \(\frac{15}{8}\) * 2 = \(\frac{15}{4}\) hours

Option E