Algebra - Working together word problem

Question

Eric and Lily are working together to paint a room, alone Eric can paint the walls 2 hours faster then Lily. If it takes them 8 hours to paint the walls when they work together how long does it take Lily is she works alone?

Answer 1

We need to set up two equations to find our unknowns. In this case, the unknowns are the time it takes Lily to paint and the time it takes Eric to paint. Let's represent these unknowns using the variables x and y

 

We know it takes them 8 hours together so x+y=8

We also know that Lily takes 2 more hours than Eric so if Eric is y then y+2=x (x represents the time it takes Lily)

 

x=time it takes Lily alone

y=time it takes Eric alone

 

We then replace the x in the first equation with the value in terms of y

x+y=8

(y+2)+y=8  (Combine the y's)

2y +2=8 (Subtract 2 from both sides)

2y=6 (Divide by 2)

y=3

 

Remember that y represents the time it takes Eric, but the question asks how long it takes Lily.

The final step is to replace the y in the first equation with our answer 3

x+y=8

x+3=8

x=5

 

So the time it takes Lily is 5 hours.  (Lily takes two more hours than Eric.)

I hope this helps!