I need help solving this problem

Question

Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 6262 minutes. Billy could mow the lawn by himself in 3030 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by himself?

Answer 1

Time together + Time together = 1

Time alone         Time alone

 

Let x = the time it takes Bobby alone

Let x-3030 = the time it takes Billy alone

 

6262 + 6262 = 1       Multiply both sides of this equation by x(x-3030).

x-3030    x

 

6262x + 6262x - 18,973,860 = x² - 3030x

12,524x - 18,973,860 = x² - 3030x

x² - 15,554x + 18,973,860 = 0

(x-6262)(x-3030) = 0

x-6262 = 0     or     x - 3030 = 0

x = 6262 minutes for Bobby    x = 3030 minutes (not logical)

x - 3030 = 6262 - 3030

x = 3232 minutes for Billy