How is this problem solved?
It takes Bobby 60 minutes longer to wax the car than it does his brother Kevin. Together it takes them 50 minutes to wax the car. How long does it take each working separately?
To solve this problem, let's set up equations based on the given information.
Let's assume that Kevin takes x minutes to wax the car. Therefore, Bobby takes x + 60 minutes.
When working together, their combined time is 50 minutes. We can express this as the following equation:
1/x + 1/(x + 60) = 1/50
Now, to solve this equation, we can use algebraic methods. We'll multiply every term in the equation by 50x(x + 60) to eliminate the denominators:
50(x + 60) + 50x = x(x + 60)
Next, distribute and simplify:
50x + 3000 + 50x = x^2 + 60x
Combine like terms:
x^2 + 60x - 100x - 100x + 3000 = 0
Simplify further:
x^2 - 90x + 3000 = 0
Now, we can solve this quadratic equation for x using factoring or the quadratic formula. Factoring is the simplest in this case:
(x - 30)(x - 100) = 0
This yields two solutions: x = 30 and x = 100.
Since it doesn't make sense for Kevin to take 100 minutes (as Bobby would then take 160 minutes), we can conclude that Kevin takes 30 minutes to wax the car and Bobby takes 90 minutes (since x + 60 = 30 + 60).
So, working separately, it takes Kevin 30 minutes and Bobby 90 minutes to wax the car.