Question

It takes Mickey a total of 45 minutes to ride his bike 5 miles to Minnie's house and then walk the remaining mile to school with her. If he rides his bike the entire distance to school at the same rate he rode to Minnie's house, it will take him 30 minutes. What is his walking speed, in miles per hour?

Answer 1

Answer:

3 miles per hour.

Step-by-step explanation:

Let x represent Mickey's walking speed in miles per hour.

We have been given that it takes Mickey a total of 45 minutes to ride his bike 5 miles to Minnie's house and then walk the remaining mile to school with her.

We can see that total distance is equal to 5 miles plus 1 mile that is 6 miles.

Since it take 30 minutes to travel a distance of 6 miles, so Mickey's biking speed would be:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

$\text{Biking speed}=\frac{6\text{ Miles}}{30 \text{ Minutes}}$

$\text{Biking speed}=\frac{6\text{ Miles}}{0.5 \text{ Hour}}$

$\text{Biking speed}=12\frac{\text{ Miles}}{\text{ Hour}}$

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$45\text{ Minutes}=\frac{5\text{ Miles}}{\frac{12\text{ Miles}}{\text{Hour}}}+\frac{1\text{ Mile}}{\frac{x\text{ Miles}}{\text{Hour}}}$

Let us convert 45 minutes into hours.

$\frac{45}{60}\text{ Hours}=\frac{5\text{ Miles}}{12\text{ Miles}}\cdot \text{Hour}+\frac{1\text{ Mile}}{x\text{ Miles}}\cdot \text{Hour}$

$\frac{3}{4}\text{ Hours}=\frac{5}{12}\cdot \text{Hour}+\frac{1}{x}\cdot \text{Hour}$

$\frac{3}{4}=\frac{5}{12}+\frac{1}{x}$

$\frac{3}{4}\cdot 12x=\frac{5}{12}\cdot 12x+\frac{1}{x}\cdot 12x$

$9x=5x+12$

$9x-5x=5x-5x+12$

$4x=12$

$x=\frac{12}{4}$

$x=3$

Therefore, Mickey' walking speed is 3 miles per hour.