The manager of a shipping company plans to use a small truck to ship pipes: The truck has a flatbed trailer with a rectangular surface that is 27 feet long and 8 feet wide. The truck will travel from Atherton to Bakersfield, where some pipes will be delivered, and then on to Castlewood to deliver the remaining pipes. The map shows the roads that connect Atherton. Bakersfield. and Castlewood.
The manager is planning to buy a new truck with better gas mileage. He collected data bout the gas mileage of one of the company's trucks. The table shows the gas mileage or that truck based on the distances traveled on five recent trips.
How many different ways can the truck travel from Atherton to Bakersfield a to Castlewood, using the roads on the map?

Rationale

There are 6 different ways the truck can travel from Atherton to Bakersfield and then to Castlewood.

The problem involves determining the number of unique routes available based on the connections between the locations on the map. By analyzing the possible paths from Atherton to Bakersfield and then to Castlewood, we can ascertain that there are indeed 6 distinct routes.

A (6) CORRECT

This option accurately reflects the total number of unique routes available for the truck to travel from Atherton to Bakersfield and then to Castlewood. Depending on the connections shown on the map, there are multiple pathways that can be taken, leading to this total.

B (8) YOUR ANSWER

This choice overestimates the number of routes available. Upon reviewing the connections on the map, it’s clear that not all potential combinations lead to new, distinct routes. Therefore, while there may be more than a few routes, 8 exceeds the actual count based on the provided connections.

C (9) YOUR ANSWER

Similar to option B, this answer also suggests too many potential routes. The calculation for determining unique paths must consider the specific intersections and connections available on the map, which do not support a total of 9 distinct routes.

D (5) YOUR ANSWER

This option undercounts the available routes. While it is close to the actual number, it fails to include all unique pathways that can be taken to travel from Atherton to Bakersfield and then to Castlewood, confirming that there are indeed more than five valid routes.

Conclusion

In summary, the number of unique routes from Atherton to Bakersfield and then to Castlewood is calculated to be 6, as confirmed by analyzing the connections on the map. This understanding of the route options is crucial for logistical planning in the shipping industry, enabling the manager to optimize travel for the company’s operations effectively.

There are 6 different ways the truck can travel from Atherton to Bakersfield and then to Castlewood.

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