Bo drove 448 miles in 7 hours. If he continued at the same rate, how long would it take to travel 1152 miles?

Steps to Solve

1. Calculate Bo's Speed

   First, we need to find Bo's speed in miles per hour (mph). To do this, we divide the distance he traveled by the time it took.

   So, the speed is: $$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{448 \text{ miles}}{7 \text{ hours}} $$

2. Determine the Time to Travel 1152 Miles

   Next, we use the speed we calculated to find out how long it will take Bo to travel 1152 miles. We can rearrange the speed formula to solve for time: $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$

   Substituting the values: $$ \text{Time} = \frac{1152 \text{ miles}}{\text{Speed}} $$

3. Substituting Speed into the Time Equation

   We can insert Bo's speed from step 1 into the equation for time: $$ \text{Time} = \frac{1152 \text{ miles}}{\frac{448 \text{ miles}}{7 \text{ hours}}} $$

   Which simplifies to: $$ \text{Time} = \frac{1152 \times 7}{448} $$

4. Calculate the Final Time

   Now we just perform the final calculation: $$ \text{Time} = \frac{8064}{448} $$

   Simplifying this gives: $$ \text{Time} = 18 \text{ hours} $$