Question

On Monday lance ran 30 min and swam 20 min. His fitness app told him he burned 610 calories. On Wednesday the fitness app told him he burned 695 calories when he ran 25 min and swam 40 min. How many calories he burned for one min?

Answer 1

Iance burned 15 calories per minute running and 8 calories per minute swimming

Explanation:

Let

x = number of calories burned per minute running

y = number of calories burned per minute swimming

On Monday

ran 30 min - burned 30x calories

swam 20 min - burned 20y calories

In total,
`30x+20y=610` calories.

On Wednesday

ran 25 min - burned 25x calories

swam 40 min - burned 40y calories

In total,
`25x+40y=695`

You get the system of two equations:

`\left\{\begin{array}{l}30x+20y=610\\ \\25x+40y=695\end{array}\right.\Rightarrow \left\{\begin{array}{l}3x+2y=61\\ \\5x+8y=139\end{array}\right.`

Multiply the first equation by 4 and subtract the second equation from the first:

`4(3x+2y)-(5x+8y)=4\cdot 61-139\\ \\12x+8y-5x-8y=244-139\\ \\7x=105\\ \\x=15`

Substitute it into the first equation:

`3\cdot 15+2y=61\\ \\45+2y=61\\ \\2y=61-45\\ \\2y=16\\ \\y=8`

Iance burned 15 calories per minute running and 8 calories per minute swimming