It takes Kevin 3 hours longer than Walter to build a tree house.Together they can do the job in 2 hours. How long would it take each man to build the tree house on his own?

Question

Would x = Walter and x + 3 =Kevin?

Answer 1

Let the time in hours to build the tree house alone be K and W, so K=W+3.

The rate (house per hour) at which they can each build a house alone is 1/(W+3) and 1/W because hours per house is the inverse of house per hour. Working together their combined rate is 1/2 house per hour, because it takes 2 hours to build one house. So, combining the rates we get 1/(W+3)+1/W=1/2. We solve this by multiplying by the LCM 2W(W+3): 2W+2(W+3)=W(W+3); 4W+6=W^2+3W; W^2-W-6=0=(W-3)(W+2), so W=3 and K=6.

SOLUTION: Kevin takes 6 hours to build the tree house by himself and Walter takes 3 hours.

Or think of it like this. The house is made of 60 pieces of wood, say. After building the house together for an hour they would have used 30 pieces of wood, Walter would have used 20 pieces and Kevin 10. So it would have taken Walter 3 hours to make the house because 3*20=60, and Kevin would have taken 6 hours because 6*10=60. Working together 2(20+10)=60.

Answer 2

By given data kevin = water +3

Per hour rate = 1/(water+3)
=> 1/(water+3)+1/water=1/2
=> water = 3

and

kevin = 3+3
kevin = 6

Walter 3 hr; Kevin 6 hr