need math help with school

Question

Twin​ brothers, Billy and​ Bobby, can mow their​ grandparent's lawn together in

115

minutes. Billy could mow the lawn by himself in

30

minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by​ himself?

Answer 1

1/x +1/(x-30) = 1/115

multiple by LCD = 115x(x-30)

115(x-30) + 115x = x^2 -30x

115x -3450+115x = x^2 -30x

x^2 -260x +3450=0170.15

x^2 -260x +130^2 = 130^2 -3450

(x-130)^2 = 16900-3450

x-130 = +/-sqr13450

x = 180+/-5sqr538

x = about 64.03 or 295.97

x = about 296 minutes for Bobby to do it alone

check the answer:

1/296 + 1/266

= 266/296(266) + 296/296(266)

= 562/296(266)

= about .01

1/115 = about .01

looks about right