For saving energy, bicycling and walking are far more efficient means of transportation than is travel by automobile. For example, when riding at 11.0 mi/h, a cyclist uses food energy at a rate of about 420 kcal/h above what he would use if merely sitting still. (In exercise physiology, power is often measured in kcal/h rather than in watts. Here 1 kcal = 1 nutritionist's Calorie = 4186 J.) Walking at 2.70 mi/h requires about 240 kcal/h. It is interesting to compare these values with the energy consumption required for travel by car. Gasoline yields about 1.30 108 J/gal.(a) Find the fuel economy in equivalent miles per gallon for a person walking.1 mi/gal(b) Find the fuel economy in equivalent miles per gallon for a person bicycling.2 mi/gal

a) 349.4 mi/gal

b) 813.4 mi/gal

Explanation:

Given,

- 1 kcal = 1 nutritionist's Calorie = 4186 J

- Walking at 2.70 mi/h requires about 240 kcal/h.

- Riding at 11.0 mi/h, a cyclist uses food energy at a rate of about 420 kcal/h

- Gasoline yields about (1.30 × 10⁸) J/gal

a) Fuel economy in equivalent miles per gallon for a person walking.

A person walking burns 240 kcal/h walking at a speed of 2.70 mi/h

In 1 hour, a person burns 240 kcal walking 2.70 mi.

Converting kcal to J

1 kcal = 4186 J

240 kcal = 240 × 4186 = 1,004,640 J

This means, 1,004,640 J is burned walking 2.7 miles.

Gasoline yields (1.3 × 10⁸) J/gal

The fuel economy is then calculated.

1,004,640 J = 2.7 miles

(1.3 × 10⁸) J/gal = [(2.7 × 1.3 × 10⁸)/1,004,640] mi/gal

(1.3 × 10⁸) J/gal = 349.4 mi/gal.

b) Fuel economy in equivalent miles per gallon for a person bicycling.

A person bicycling burns 420 kcal/h cycling at a speed of 11.0 mi/h

In 1 hour, a person burns 420 kcal bicycling 11.0 mi.

Converting kcal to J

1 kcal = 4186 J

420 kcal = 420 × 4186 = 1,758,120 J

This means, 1,758,120 J is burned bicycling 11.0 miles.

Gasoline yields (1.3 × 10⁸) J/gal

The fuel economy is then calculated.

1,758,120 J = 11.0 miles

(1.3 × 10⁸) J/gal = [(11 × 1.3 × 10⁸)/1,758,120] mi/gal

(1.3 × 10⁸) J/gal = 813.4 mi/gal.

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