Problema Solution
Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 61 minutes. Billy could mow the lawn by himself in 21 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by himself?
Answer provided by our tutors
let
x = the minutes Billy needs to mow the lawn alone, x > 0
y = the minutes Bob needs to mow the lawn alone, y > 0
Billy could mow the lawn by himself in 21 minutes less time that it would take Bobby
x = y - 21
together they can mow their grandparent's lawn in 61 minutes
the rate of Billy (1 lawn in x min) + rate of Bobby (1 lawn in y min) = the together rate (1 lawn in 61 min)
1/x + 1/y = 1/61
plug x = y - 21 into the last equation
1/(y - 21) + 1/y = 1/61
by solving we find 2 roots
y1 = 133.4 min
y2 = 9.6 min
y2 = 9.6 min is not the solution since for y2 = 9.6 min we have x = 9.6 - 21 < 0 and that is not possible (we need x to be positive)
click here to see the step by step solution of the equation
It would take 133.4 min for Bobby to mow the lawn by himself.