Question

A painter can paint a kitchen in 14 hours. An apprentice can paint the same kitchen in 35 hours. If they worked together, how long would it take them to paint the kitchen?

Answer 1

In one hour the painter who paints the kitchen in 14 hours paints 1/14 of the kitchen and the other painter paints 1/35 of the kitchen. Let t= the time it takes for both of them working together. Then (1/14)t is the portion of the task completed by the first painter and (1/35)t is the portion completed by the other painter. Thus,

(1/14)t+(1/35)t=1

since the portions must add to 1 complete task.

Multiply both sides by 70 to yield

5t + 2t = 70 or

t=10 hours.

Answer 2

In 1 hr 1st painter paints 1/14 of the kitchen
In 1 hr 2nd one paints 1/35
Both can paint in 1 hr=(1/34)+(1/14)=7/70=1/10 of the kitchen
The time they takes to paint 1/10 of the kitchen is 1 hr
10/10 or total=10 hr