Site map 

 Contact Graeme 

 Skip Navigation LinksMath Help > Math Puzzles > 2004 State Logic Quiz > Question 03 > Question 03

Academic Decathlon 2004 State Championship Logic Quiz

Question 03

Arthur and Peter built a brick house in 24 days.  If Arthur works two thirds as quickly as Peter, how long would each person alone take to build a brick house?


Arthur could build the house in 60 days, and Peter could build it in 40 days.

Let x be the speed that Peter works, measured in houses per day.

Arthur works at a speed of (2/3) x.

So their total working speed is x + (2/3) x, which is (5/3) x.  Since they can build one house in 24 days, we know they can build 1/24 houses per day, working together.  In other words,

(5/3) x = 1/24

Equating the means and the extremes, we simplify this as follows:

(5/3) x = 1/24
5x / 3 = 1 / 24
3 = 120x
1/40 = x

So Peter can build 1/40 houses per day, or one house every 40 days.

Arthur works at 2/3 the speed of Peter, so he can build (2/3)(1/40) = 1/60 houses per day, or one house every 60 days.


Related pages in this website

See the NEXT puzzle in the Academic Decathlon 2004 Logic Quiz


The webmaster and author of this Math Help site is Graeme McRae.