How long would it take Bobby to mow the lawn by himself?

Question

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

69 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/x + 1/y = 1/69

x = y-25 = time for billie to mow the lawn by himself

y= time for bob to mow the lawn by himself

1/(y-25) + 1/y = 1/69

eliminate the fractions, multiply by LCD= 69y(y-25)

69y + 69(y-25) = y(y-25)

69y + 69y - 69(25) = y^2 -25y

y^2 - 163y + 1725 = 0

solve for y using the quadratic formula, or factor if possible

y = 163/2 + .5sqr(163^2 -4(1725))= 81.5 +/- .5sqr19669= about 81.5+/-70.5=11.5, 152.ignore 11.5 as it makes x negative

x =y-25= 152-25= 127

billie can mow alone in about 127 minutes

bob can mow alone in about 152 minutes

together in 69 minutes

check the answers

1/127 + 1/152 = about .014

1/69 = about .014

127= about 2 hours

152 min = about 2 1/2 hours

69 min= about 1 hour

1/2 + 1/2.5 = 1/2+2/5 = 5/10+4/10 = 9/10 = about 10/10 = 1 hour together

the answers are in the right range of time