Question

Mario and Kenneth are in a car wash station. The time that Mario takes in washing a car alone is 20 minutes less than the time that Kenneth takes in washing the same car. If both of them work together in washing a car, it will take them 90 minutes. How long will it take each of them to wash a car?

Option 1: Mario takes 60 minutes, Kenneth takes 80 minutes.
Option 2: Mario takes 70 minutes, Kenneth takes 90 minutes.
Option 3: Mario takes 45 minutes, Kenneth takes 65 minutes.
Option 4: Mario takes 50 minutes, Kenneth takes 70 minutes.

Answer 1

Mario takes 45 minutes, Kenneth takes 65 minutes.

Step-by-step explanation:

Let's assume that Kenneth takes x minutes to wash the car. According to the given information, Mario takes 20 minutes less than Kenneth. So, Mario takes (x-20) minutes to wash the car.

When they work together, they can wash the car in 90 minutes. We can set up the equation:

[1/(x-20)] + [1/x] = 1/90

To solve this equation, we can multiply through by x(x-20) to clear the fractions:

x + (x-20) = x(x-20)/90

Simplifying the equation gives us:

2x - 20 = (x² - 20x)/90

By cross-multiplying and rearranging, we get:

x² - 20x - 180x + 20 = 0

Simplifying further, we get:

x² - 200x + 20 = 0

Using the quadratic formula, we get:

x = (-b +/- √(b² - 4ac))/2a

Substituting the values a, b, and c into the formula gives us:

x = (200 +/- √(200² - 4*1*20))/2*1

Simplifying further, we get:

x = (200 +/- √(40000 - 80))/2

x = (200 +/- √(39920))/2

x = (200 +/- 199.799)/2

So, x = 199.799/2 or x = 200.201/2

Therefore, it will take each of them approximately 99.90 minutes (option 3) to wash the car.