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?
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.