Roberto decorates retangular signs. One sign is 2/3 foot long and 1/4 foot wide. Another sign is 1/2 long and 1/3 foot wide. It takes Roberto 3/4 hour to decorate 1 square foot sign. What is the total amount of time, in hours, it takes Roberto to decorate both signs?

It'll take him 1/4 hours to decorate the two signs.

Step-by-step explanation:

In order to know how long Roberto will take to decorate all the signs we need to find their surface area, since they're rectangular their area is given by the product of their dimensions.

First sign:

area1 = (2/3) * (1/4) = 2/12 = 1/6 foot²

Second sign:

area2 = (1/2) * (1/3) = 1/6 foot²

The total area he has to paint is the sum of their individual areas, so we have:

total area = area1 + area2 = 1/6 + 1/6 = 2/6 = 1/3 foot²

To find out how long he'll take to decorate this area we can use a rule of three as shown bellow:

3/4 hour - > 1 foot²

x hour - > 1/3 foot²

x = (3/4) * (1/3) = 1/4 hours