 # Problem of the Week Problem B and Solution Road Trip

## Problem

Mr. Sand is going on a trip to the beach. The total distance to the beach is $$263$$ km. His car has a $$60$$ L gas tank and can travel $$640\,000$$ m on that tank of gas.

Suppose that there are two service stations available to Mr. Sand. Station A charges $$\40$$ for $$25$$ L of gas, while Station B charges $$\51$$ for $$30$$ L of gas.

Determine the cost of the gas for his trip if he fills up at Station A versus the cost if he fills up at Station B. Which is the more economical? ## Solution

If his vehicle has a $$60$$ L gas tank and will travel $$640\,000$$ m or $$640$$ km on one full tank, then he is using $$60 \div 640 = 0.09375$$ L of gas per km.

Since the distance to the beach is $$263$$ km, then this trip will take $$263\times 0.09375\approx 24.656$$ L of gas.

For Station A:

The cost is $$\40$$ for $$25$$ L. Therefore, the gas will cost $$\frac{40}{25} = \1.60$$ per L.

Thus, the cost of the trip for Station A is $$24.656 \times \1.60 = \39.45$$.

For Station B:

The cost is $$\51$$ for $$30$$ L. Therefore, the gas will cost $$\frac{51}{30} = \1.70$$ per L.

Thus, the cost of the trip for Station B is $$24.656 \times \1.70 = \41.92$$.

Therefore, Station A is more economical than Station B.

Note: Since the gas at Station A costs less per L than at Station B, then using gas from Station A will always cost less than using gas from Station B.