You have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both machines. How much time should you spend on each machine? Explain it briefly from given data and calculate.
The Correct Answer and Explanation is:
To solve this problem, we need to divide 40 minutes of exercise time between two machines so that 300 calories are burned in total. However, you haven’t provided the calories burned per minute on each machine, which is essential to solve the problem accurately. So, let’s assume the following common gym scenario:
- Treadmill burns 10 calories per minute
- Stationary bike burns 5 calories per minute
Step 1: Let Variables Represent Time
Let:
- x = minutes on treadmill
- y = minutes on stationary bike
Given:
- Total time:
x + y = 40 → Equation ① - Total calories burned:
10x + 5y = 300 → Equation ②
Step 2: Solve the System of Equations
From Equation ①:
y = 40 – x
Substitute into Equation ②:
10x + 5(40 – x) = 300
10x + 200 – 5x = 300
5x = 100
x = 20
Now find y:
y = 40 – x = 40 – 20 = 20
✅ Final Answer:
- 20 minutes on treadmill
- 20 minutes on stationary bike
🧠 Explanation (300+ words):
This problem is a classic example of solving a system of linear equations, commonly encountered in real-life fitness planning. You’re given a total time constraint (40 minutes) and a calorie-burning goal (300 calories). The challenge is to determine how to distribute your time between two different cardio machines with different calorie-burning rates.
We begin by assigning variables to the unknowns: time on each machine. The treadmill burns calories at a faster rate (10 calories per minute), while the stationary bike burns fewer (5 calories per minute). Therefore, we set up two equations:
- One for the total time:
x + y = 40 - One for total calories:
10x + 5y = 300
These equations represent constraints that must be satisfied simultaneously. By substituting the first equation into the second, we eliminate one variable and solve for the other. This leads us to a unique solution: 20 minutes on each machine.
This balanced time split ensures that the total workout doesn’t exceed 40 minutes and the total calories burned add up to 300. You burn 200 calories on the treadmill (20 × 10) and 100 on the bike (20 × 5), totaling 300.
This method is both practical and mathematically sound. It can be adjusted based on different machines or goals, making it a versatile problem-solving approach in fitness planning.