Zeno takes 20 min longer to decorate a dozen cupcakes than it takes Lia. When they work​ together, it takes them 49.5 min. How long would each take to do the job​ alone?

Answer 1

Lia =x Zane = x+20

equation 1/x + 1/x+ 20 = 1/4.95 LCD= 4.95 (x) (x+20) multiply both sides of the equation and cancel out

common factors

4.95 x + 990+ 4.95 x= X^2 +20x put all the terms on one side

0= x^2-79x-990

0=(x-90)(x+11)

x=90 ,x= -11

Lia takes 90 minutes to do the job alone and Zeno takes 90+20 minutes = 110 minutes to do the job alone.