On a trip from Virginia to Florida, the Sampson family wants to
travel at least 420 miles in 8 hours of driving. What must be their
average rate of speed? Write as an inequality 

To find the average speed the Sampson family must maintain, we use the formula for distance:

\[
\text{Distance} = \text{Rate} \times \text{Time}
\]

Let \( r \) represent the average rate of speed in miles per hour. The family wants to travel at least 420 miles, so the inequality would be:

\[
r \times 8 \geq 420
\]

Now, solve for \( r \) by dividing both sides of the inequality by 8:

\[
r \geq \frac{420}{8}
\]

\[
r \geq 52.5
\]

Thus, the Sampson family must maintain an average speed of at least **52.5 miles per hour** to travel 420 miles in 8 hours.

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### Related Questions:
1. If they want to drive 500 miles in 8 hours, what would their required speed be?
2. What would happen to the required speed if they had to travel the 420 miles in 7 hours instead?
3. How many miles would they travel if they drove for 8 hours at 60 mph?
4. What if they drove at a consistent speed of 52 mph? Would they still reach 420 miles in time?
5. How would adding a 1-hour break affect the minimum required speed?

### Tip:
Always check if the distance given in a problem corresponds to the time and speed for accurate planning!

On a trip from Virginia to Florida, the Sampson family wants to travel at least 420 miles in 8 hours of driving. What must be their average rate of speed? Write as an inequality.

Learn how to calculate the minimum average speed needed for the Sampson family to travel 420 miles in 8 hours. This problem uses algebraic inequalities and the distance-rate-time formula. Suitable for students in Grades 6-8.

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