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?
If Kevin takes x minutes,
1/50 = 1/(x+60) + 1/x
x = 10(2+√34) =~ 78.3
So
Kevin takes 78.3 minutes,
Bobby takes 138.3 minutes.
Thank you.
To solve this problem, we can set up a system of equations based on the given information.
Let's say it takes Kevin x minutes to wax the car. Then, it would take Bobby x + 60 minutes to wax the car.
When they work together, they can complete the job in 50 minutes, so we can write the equation:
1/x + 1/(x + 60) = 1/50
To solve this equation, we can multiply through by 50x(x + 60) to eliminate the fractions:
50(x + 60) + 50x = x(x + 60)
Simplifying the equation, we get:
50x + 3000 + 50x = x^2 + 60x
Combining like terms, we have:
x^2 + 60x - 100x - 3000 = 0
Simplifying further, we get:
x^2 - 40x - 3000 = 0
Now, we can factor the quadratic equation or use the quadratic formula to find the values of x. Factoring, we get:
(x - 60)(x + 50) = 0
So, x = 60 or x = -50
Since time cannot be negative in this context, we ignore the value x = -50.
Therefore, it takes Kevin 60 minutes to wax the car, and it takes Bobby 60 + 60 = 120 minutes to wax the car when working separately.