To solve this problem, let's define two variables:
- Let \( x \) be the duration (in hours) of Plan A.
- Let \( y \) be the duration (in hours) of Plan B.
For Wednesday
On Wednesday, there were:
- 4 clients doing Plan A
- 8 clients doing Plan B
The total hours spent on Wednesday can be represented by the equation: \[ 4x + 8y = 17 \]
For Thursday
On Thursday, there were:
- 2 clients doing Plan A
- 3 clients doing Plan B
The total hours spent on Thursday can be represented by the equation: \[ 2x + 3y = 7 \]
Now we have a system of equations:
- \( 4x + 8y = 17 \) (Equation 1)
- \( 2x + 3y = 7 \) (Equation 2)
Step 1: Simplifying the equations
First, we can simplify Equation 1 by dividing all terms by 4: \[ x + 2y = \frac{17}{4} \] or, \[ x + 2y = 4.25 \quad \text{(Equation 3)} \]
Step 2: Solve the system of equations
Now, we can use Equation 2 and Equation 3 together.
From Equation 3: \[ x = 4.25 - 2y \]
Substituting \( x \) in Equation 2: \[ 2(4.25 - 2y) + 3y = 7 \] \[ 8.5 - 4y + 3y = 7 \] \[ 8.5 - y = 7 \] \[ -y = 7 - 8.5 \] \[ -y = -1.5 \] \[ y = 1.5 \]
Step 3: Find \( x \)
Now we can use the value of \( y \) to find \( x \): \[ x = 4.25 - 2(1.5) \] \[ x = 4.25 - 3 \] \[ x = 1.25 \]
Conclusion
The durations of the workout plans are:
- Plan A lasts for 1.25 hours (or 1 hour and 15 minutes).
- Plan B lasts for 1.5 hours (or 1 hour and 30 minutes).