SOLUTION: I am helping my daughter do her homework and we are stuck on this one. Please help me explain it. Twin brothers, person A and person B can mow the lawn together in 20 minutes.

Question 862073: I am helping my daughter do her homework and we are stuck on this one. Please help me explain it.
Twin brothers, person A and person B can mow the lawn together in 20 minutes. Person A can mow the lawn by himself in 9 minutes less than it would take person B. How long would it take person B to mow the lawn by himself?
Many thanks,

Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A & B can mow the lawn in 20 minutes
consider mowing the lawn is one job
so they do 1/20 of the job in 1 minute

let B take x minutes to do the job alone
he does 1/x of the job in 1 minute
A takes 9 minutes less than B (x-9)
So A does 1/(x-9) of the job in 1 minute
Together

LCM 20x(x-9)
20(x-9)+20x=x(x-9)
20x-180+20x=x^2-9x
x^2-49x+!80=0
x^2-45x-4x+!80=0
x(x-45)-4(x-45)=0
(x-45)(x-4)=0
x=45 OR 4
B takes 45 minutes to mow the lawn alone

so he does 1/9 of the job in 1 minute

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The rates of each brother are added when they work on the lawn at the same time. Use the rates as LAWNS per MINUTE.
A, 1/something
B, jobs per minute
A,
A plus B, 1/20 jobs per minute, .
Note that 1 lawn is the same as 1 job.

EQUATION:

Solve for x, which is the time for brother B to do the 1 job alone, himself.

Multiply by x(x-9) both sides,

Check discriminant, D=49^2-4*180=2401-720=1681, a positive value.
This is actually , not at all obvious.
-
continuing,
, we use the positive square root form, because it will make sense.

This means, brother B mows the one lawn alone by himself in 45 minutes.
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