Question

Sean can paint a house in $10$ hours, and Dan can paint the same house in $12$ hours. If Sean begins the job and does $\frac{1}{3}$ of it and then Dan takes over and finishes the job, Calculate the total time it takes them to paint the house.

• A. $10$ hours, $40$ minutes
• B. $11$ hours
• C. $11$ hours, $20$ minutes
• D. $11$ hours, $40$ minutes
• E. $12$ hours

Answer 1

The correct option is C $11$ hours, $20$ minutes

Sean can paint a house in $10$ hours and Dan can paint a house in $12$ hours.

Now Sean paints ${\left(\frac{1}{3}\right)}^{rd}$ house and Dan paints ${\left(\frac{2}{3}\right)}^{rd}$ house

Time taken by sean to paint ${\left(\frac{1}{3}\right)}^{rd}$ house is $\frac{10}{3}$ hours
Time taken by dan to paint ${\left(\frac{2}{3}\right)}^{rd}$ house is $\frac{2}{3}\times 12=8$ hours
Total time is $\frac{10}{3}+8=\frac{34}{3}$ hours, which means $11$ hours , $20$ minutes.