Q. 351 - Intermediate Algebra

Question

Leroy spent $20$ minutes jogging and $40$ minutes cycling and burned $600$ calories. The next day,

Leroy swapped times, doing $40$ minutes of jogging and $20$ minutes of cycling and burned the same

number of calories. How many calories were burned for each minute of jogging and how many

for each minute of cycling?

Step-by-Step Solution

Answer

The number of calories burned for jogging in each minute is$10$.

The number of calories burned for cycling in each minute is$10$.

Step 1. Given information

Leroy spent $20$ minutes jogging and $40$ minutes cycling and burned $600$ calories.

At the next day, Leroy spent $40$ minutes jogging and $20$ minutes cycling and burned the same number of calories.

Step 2. Forming two linear equations using two given conditions

Let $x$ represents the number of calories burned for jogging in a minute,

Let $y$ represents the number of calories burned for cycling in a minute,

Using first condition, we get eq.(i) as

$$\begin{gathered} 20x+40y=600 \\ x+2y=30 \end{gathered}$$

Using next day condition, we get eq.(ii) as

$$\begin{gathered} 40x+20y=600 \\ 2x+y=30 \end{gathered}$$

Step 3. Find value of x and y by solving linear equations using substitution method

Using eq.(i), find $x$

$$\begin{gathered} x+2y=30 \\ x=30-2y \end{gathered}$$

Substitute this value of $x$ in eq.(ii),

$$\begin{gathered} 2x+y=30 \\ 2(30-2y)+y=30 \\ 60-4y+y=30 \\ 60-3y=30 \\ 3y=30 \\ y=10 \end{gathered}$$

Now substitute this value of $y$ in any of the equation,

$$\begin{gathered} x+2y=30 \\ x+2\left(10\right)=30 \\ x+20=30 \\ x=10 \end{gathered}$$

Step 4. Check by substituting values in both the equations

Substitute $x=10,y=10$ in both the equations

$$\begin{gathered} x+2y=30 \\ 10+2\left(10\right)=30 \\ 30=30 \end{gathered}$$

This is true

$$\begin{gathered} 2x+y=30 \\ 2\left(10\right)+10=30 \\ 30=30 \end{gathered}$$

This is true

Step 5. Required answer

The number of calories burned for jogging in each minute is $10$.

The number of calories burned for cycling in each minute is $10$.