Juan walks 3.5 miles in 56 minutes. How long will it take him to walk 1 mile?

Steps to Solve

1. Calculate Juan's speed in miles per minute

To find Juan's speed, we divide the total distance he walks by the total time it takes him. $$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$ $$ \text{Speed} = \frac{3.5 \text{ miles}}{56 \text{ minutes}} $$

2. Simplify the fraction

Divide both the numerator and the denominator by 7. $$ \text{Speed} = \frac{3.5 \div 7}{56 \div 7} = \frac{0.5}{8} \text{ miles per minute} $$

3. Find the time it takes to walk 1 mile

To find the time it takes to walk 1 mile, we take the inverse of the speed (i.e. $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$). Since we want to find the time to walk 1 mile: $$ \text{Time} = \frac{1 \text{ mile}}{\frac{0.5}{8} \text{ miles per minute}} $$ $$ \text{Time} = 1 \div \frac{0.5}{8} = 1 \times \frac{8}{0.5} = \frac{8}{0.5} \text{ minutes} $$

4. Simplify the fraction

Multiply both the numerator and denominator by 2 to remove the decimal: $$ \text{Time} = \frac{8 \times 2}{0.5 \times 2} = \frac{16}{1} = 16 \text{ minutes} $$