**Problem of the Week**

Problem B and Solution

Fare’s Fair!

**Problem**

Three brothers, Andy, Bob, and Curly, take a taxi together home from the airport.

Their homes lie along the same route;

Andy’s is \(21\) km from the airport,

Bob’s is \(42\) km, and

Curly’s is \(63\) km.

If the taxi fare is $2.00 per km, try to find at least two possible fair ways for each of the three travellers to pay the driver (not including the tip)?

**Solution**

The total cost is \(\$2\) per km \(\times\ 63\) km \(= \$126\). Here are three possible ways to pay the driver.

Solution 1:

If each passenger pays \(\frac{1}{3}\) of the total cost, then they each pay \(\$126 \div 3 = \$42\).

Solution 2:

Three passengers travel the first \(\frac{1}{3}\) of the trip (21 km) for $42, so each pays \(\$42 \div 3 = \$14\) for that portion of the trip. So Andy pays $14.

Two passengers travel the next 21 km for $42, so each pays \(\$42\div 2 = \$21\) each for that portion of the trip plus \(\$14\) for the first portion of the trip. So Bob pays \(\$21 + \$14 = \$35\).

Only one passenger, Curly, travels the final 21 km for $42. So Curly pays \(\$14 + \$21 + \$ 42 = \$ 77\) for all three portions of the trip.

Notice the total paid is \(\$14 + \$35 + \$77 = \$126\).

Solution 3:

A third possibility is that they each pay according to their distance travelled. Andy travels 21 km, Bob travels 42 km, and Curly travels 63 km, a total of \(21 + 42 + 63 = 126\) km. Thus it would cost \(\$126 \div 126\) km \(= \$1.00\) per km per person. So Andy pays $21, Bob pays $42, and Curly pays $63.