Twin brothers Billy and Bobby can mow their grandparents law

Twin brothers, Billy and Bobby, can mow their grandparent\'s lawn together in 90 minutes, Billy could mow the lawn by himself in 15 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by himself? It would take Bobby minutes to mow the lawn by himself (Round to the nearest minute.)

Solution

work done in 1 min if both worked together

(B1 + B2) one hour\'s work = W/90

bobby\'s one minute\'s work = W/b

where b = total minute taken by bobby

billy\'s one minute\'s work = W/(b-15)

which means

W/90 = W/b + W/(b - 15)

1/90 = 1/b + 1/(b - 15)

b^2 - 15b = 90b - 1350 + 90b

b^2 - 195b + 1350 = 0

Solving the equation

k = 187.81 min