Question

Your uncle Karl wants to lose some weight by burning extra calories each week (2kg = approx. 3000 calories). He will do it by riding a bicycle, which burns 350 calories an hour, and by walking, which turns 200 calories an hour. If uncle Karl has 10 hours per week to devote to exercise, what combination of walking and cycling will allow him to achieve his goal of burning exactly 3000 calories?

Answer 1

Answer:

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Answer 2

Given:

No. of calories to burn by Karl = 3000

No. of calories burnt per hour by walking = 200

No. of calories burnt per hour by cycling = 350

No. of hours per week for Karl = 10

To find:

No. of hours required to exercise through walking and cycling for burning 3000 calories.

Solution:

Let W be the no. of hours required to burn calories in one hour by walking.

Let C be the no. of hours required to burn calories in one hour by cycling.

Formulating the given information,

$W+C=10...(1)\\200W+350C=3000...(2)$

Multiplying equation (1) by 200

$200W+200C=2000...(3)$

Subtracting equation (3) from equation (2)

$150C=1000$

$C=\frac{1000}{150}$

$C$ ≈ $7$

Substituting in equation (1)

$W+C=10$

$W+7=10$

$W=10-7$

$W=3$

∴ $W=3, C=7$

Final Answer:

Karl has to spent 7 hours of cycling and 3 hours of walking per week to burn exactly 3000 calories.