frank can wash the car in 2/3 the time his younger brother,joe,can wash the car.they worked together and washed the car in 40 minutes.how long would it have taken each boy working separately?

X min. = Joe's time.

2x/3 = Frank's time.

1/x + 3/2x = 1/40
Multiply both sides by 2x:
2 + 3 = x/20
x/20 = 5
X = 100 min. = Joe's time.
2x/3=200/3 = 66.67 min. = Frank's time.

To solve this problem, we can break it down into steps:

Step 1: Understand the given information.
- Frank can wash the car in 2/3 the time his younger brother Joe can wash the car.
- They worked together and washed the car in 40 minutes.

Step 2: Assign variables.
Let's assign variables to represent the time each boy takes to wash the car separately.
- Let's represent Frank's time as x (in minutes).
- Since Frank can wash the car in 2/3 the time Joe takes, we can represent Joe's time as (3/2)x (in minutes).

Step 3: Set up an equation.
Since they worked together and finished washing the car in 40 minutes, we can set up the following equation:
1/x + 1/(3/2)x = 1/40

Step 4: Solve the equation.
To solve the equation, we can find a common denominator for the fractions. The common denominator will be 2/3x:
(2/3x) + (2/3x) = 1/40

Now we can add the fractions together:
(4/3x) = 1/40

To solve for x, we can cross-multiply:
4x = 3(40)
4x = 120
x = 30

So, Frank takes 30 minutes to wash the car by himself.

To find out Joe's time, we can substitute the value of x into (3/2)x:
(3/2)x = (3/2)(30)
(3/2)x = 45

Therefore, Joe takes 45 minutes to wash the car by himself.

Hence, it would have taken Frank 30 minutes and Joe 45 minutes to wash the car separately.