#
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
StationĀ 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.