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.