someone help please!

Question

Twin brothers, person A and person B, can mow their grandparent's lawn together in 12 minutes. Person A could mow the lawn by himself in 7 minutes less than it would take person B. how long would it take person B to mow the lawn by himself?

Answer 1

Let x = number of minutes that it takes person B to mow the lawn by himself

 

Then, x-7 = number of minutes for person A to mow the lawn by himself

 

1/x = portion of lawn mowed by B per minute

1/(x-7) = portion of lawn mowed by A per minute

1/12 = portion of lawn mowed by both A and B per minute

 

1/x + 1/(x-7) = 1/12

 

12(x-7) + 12x = x(x-7)

 

x² - 31x + 84 = 0

 

(x-28)(x-3) = 0

 

x = 28 or x = 3

 

x can't be 3.  Otherwise, x-7 would be negative.  

 

Therefore, x = 28 minutes.

 

Answer 2

Hello Bill

 

A and B can mow the lawn together in 12 minutes;  A + B = 12 (equation 1)

 

A can mow the lawn 7 minutes less than B;  A = B - 7 (equation 2)

 

Substitute A = B - 7 in equation 1, you get

 

B - 7 + B = 12

 

Solve for B

 

2B = 19

 

B = 19/2 = 9.5 minutes