The following table shows distances in miles between some cities in the United States. The distances have been written in scientific notation. Atlanta Baltimore Boston Chicago Los Angeles Seattle Tampa Atlanta 0 9.2735×102 1.50511×103 9.444×102 3.10801×103 3.50307×103 6.7037×102 Baltimore 9.2735×102 0 5.7785×102 9.7323×102 3.72245×103 3.7441×103 1.37072×103 Boston 1.50511×103 5.7785×102 0 1.36663×103 4.16643×103 3.99708×103 1.90293×103 Chicago 9.444×102 9.7323×102 1.36663×103 0 2.79980×103 2.78657×103 1.61477×103 Los Angeles 3.10801×103 3.72245×103 4.16643×103 2.79980×103 0 1.5442×103 3.45696×103 Seattle 3.50307×103 3.7441×103 3.99708×103 2.78657×103 1.5442×103 0 4.06249×103 Tampa 6.7037×102 1.37072×103 1.90293×103 1.61477×103 3.45696×103 4.06249×103 0

### Word Problem

A travel agency is planning a road trip tour across several cities in the United States. They have two types of vehicles: Standard vans that can hold up to 7 passengers and Luxury vans that can hold up to 12 passengers.

They need to calculate how many standard vans are needed for a trip from Atlanta to Los Angeles if a group of 54 tourists will be traveling. Given the distance from Atlanta to Los Angeles is approximately 3.10801 × 10³ miles, the travel agency wants to determine how many standard vans they will require while also ensuring that each van is filled to capacity.

If the total number of passengers traveling is 54, how many standard vans will they need for the trip?

### Solution

To calculate the number of standard vans required, we can use the formula:

\[
\text{Number of Vans Needed} = \frac{\text{Total Number of Passengers}}{\text{Capacity of One Van}}
\]

Where:
- Total Number of Passengers = 54
- Capacity of One Standard Van = 7

Now, substituting the values into the formula:

\[
\text{Number of Vans Needed} = \frac{54}{7} \approx 7.714285714285714
\]

Since you cannot have a fraction of a van, we round this number up to the next whole number.

Hence, the number of standard vans needed:

\[
\lceil 7.714285714285714 \rceil = 8
\]

### Conclusion

The travel agency will need **8 standard vans** to accommodate the 54 tourists traveling from Atlanta to Los Angeles.