Question

At the gym, mandi ran 2 miles on the treadmill and then hiked 5 miles burning a total of 370 calories. If mandi burns 17 more calories running than she does biking, how many calories does she burn each mile that she bikes

Answer 1

Mandi burns 35.3 calorie/mile by hiking.

Explanation:

Let, Mandi burns calories by running at the rate of x calorie/mile

and, she burns calories by hiking at the rate of y calorie/mile.

Then, according to the question,

2x + 5y = 370 ------------(1)

and 2x - 5y = 17 ---------(2)

So, adding (1) and (2) we get,

4x = 387

⇒ x = 387/4 = 96. 75 -------------(3)

Putting the value of x in (1) we get,

5y =
`370 - 2 *  96.75`

⇒ 5y = 370 - 193.5 = 176.5

⇒ y = 176.5/5 = 35.3 ---------(4)

So, Mandi burns 35.3 calorie/mile by hiking.

Answer 2

48 calories/mile hiking/biking

Explanation:

Let x be calories burned per mile running

Let y be calories burned per mile hiking

i. 2x + 5y = 370

ii. x - y = 17

//////////////////////////////////////////////////////////////

From eq. ii,

x - y = 17

iii. x = 17 + y

/////////////////////////////////////////////////////////////

By using substitution on eq. i, from eq. iii

2(17 + y) + 5y = 370

34 + 2y + 5y = 370

7y = 370 - 34

7y = 336

y = 336/7

y = 48 calories/mile hiking

Putting value of y in eq. iii,

x = 17 + 48

x = 65 calories/mile running