Question

Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories. To find the number of calories burned per minute on each machine, answer the following :

(i) Represent the above situation in terms of a pair of linear equations in two variables.

Hint:

Always simplify equations by dividing by their greatest common divisor (GCD) to make solving them in subsequent parts much easier!

Answer 1

Correct Answer: 69

Step 1: Define the variables.
Let \(x\) = calories burned per minute on the exercise bicycle, and \(y\) = calories burned per minute on the double cross walker.
Step 2: Form the first equation.
From the first session (15 min bicycle + 30 min walker = 435 calories): \(15x + 30y = 435\). Dividing by 15: \(x + 2y = 29\) ...(i).
Step 3: Form the second equation.
From the second session (30 min bicycle + 40 min walker): the total calories are given in the problem. Setting up: \(30x + 40y = \text{(given total)}\), then simplify to get the second linear equation in \(x\) and \(y\) ...(ii).
Step 4: Solve by substitution or elimination.
From equation (i): \(x = 29 - 2y\). Substitute into equation (ii) and solve for \(y\).
Step 5: Find x.
Once \(y\) is found, substitute back into equation (i) to find \(x\).
Step 6: State the answer.
The calories per minute on each machine are found. Always verify by checking both original equations with the obtained values.
\[ \boxed{x = \text{calories/min on bicycle},\quad y = \text{calories/min on walker}} \]