algebra quadratic equation

Question

Twin​ brothers, Billy and​ Bobby, can mow their​ grandparent's lawn together in 96 minutes. Billy could mow the lawn by himself in 25 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by​ himself?

Answer 1

1/(b-25) + 1/b = 1/96

multiply both sides by 96(b^2-25b)

96b + 96b-(96)(25) = b^2 -25b

b^2 -217b + 2400 = 0

b = 217/2 + or - (1/2)sqr(217^2 -4(2400))

= 108.5 + or - .5sqr37489

= about 108.5 + or - 193.6/2

= 108.5 + or - 96.8

= 205.3, 11.7

b-25 = 180.3 min = billy's time

b= 205.3 minutes = bobby's time

if they worked at the same rate, they'd both do it in 96x2 = 192 minutes which is about the average of what they did