Question

Jones can paint a car in 8 hours. Smith can paint the same car in 6 hours. They start to paint the car together. After 2 hours, Jones leaves for lunch and Smith finishes painting the car alone. How long does it take Smith to finish?

Answer 1

Jones takes 8 hours , therefore in one hour he paints a fraction of 1/8
smith takes 6 hours, thus in one hour he paints a fraction of 1/6
When working together they paint a fraction of 7/24 in an hour.
After 2 hours they will have painted a fraction of (7/24) ×2 = 7/12
The remainder will be 5/12 which will be undertake by smith alone.
Smith will therefore take 5/12 ×6/1 = 2.5 hour or 2 hours 30 minutes

Answer 2

Jones paints 1 car in 8 hours, so in 2 hours he can paint 2/8 th that is 1/4 th part of the car. Similarly Smith can paint 1 car in 6 hours. So in 2 hours he can paint 2/6 th that is 1/3rd of the car. When they start painting a car together they will finish (1/4 + 1/3) part of the car in 2 hours which equals to 7/12. So they finished 7/12 part of the cars painting. So what part of the car is left to be painted (1-7/12) which equals to 5/12. So smith has to paint the remaining 5/12 part of the car to finish the full painting. It takes 6 hours to complete the full car painting on his own. So it will take (5/12 multiplied by 6) amount of time to finish the rest painting which equal 5/2 hours or 2.5 hours.