# Can the car or the bike travel further?

There is a car and a motor-bike. The car and the bike both have an spare tire. Now, the car has a total of 5 tyres (one spare tire included) and the bike has a total of 3 tires (one spare tire included).

Each tire of the bike and the car will last for 100 KMs. Take the following points into consideration:

• The tire will not have any puncture or problem
• The tire will rotate only when the vehicle moves.
• Assume that petrol/diesel is infinite.
• You cannot buy new tire.
• Tires can be changed easily.
• Once a tire has been used for travelling 100 KM, it cannot be used again.

Can the car or the bike travel further?

Is this a trick question? It look just to be a math problem.

The bike can travel further.

How to travel with bike:

The bike can travel 150 km = 100 km / 2 * 3 by rotating between its wheels. For each 50 km, two of the three wheels are used, so each wheel it used for two of the intervals.

How to travel with car:

The car can travel 125 km = 100 km / 4 * 5 by using a different four of the five wheels for each of five 25 km segments.

Alternative short argument:

Alternatively, the spare tire is a +1/4 relative increase in tire-power for the car and a +1/2 for the bike, so the bike wins.

• The bike can also travel on one tire. ;)
– Harv
Jan 10, 2015 at 10:13
• @Harv And the car on 2 ;c) (...as proven in some movies...) Jan 10, 2015 at 10:29
• @Xnor: I think it is just a math's puzzle. It may be rather easy, but I think it is a valid puzzle never-the-less and to be taken seriously. (The bike requires the 'change half-way' trick to be thought of.) Please put your answer in spoiler tags. Jan 10, 2015 at 10:32
• The case with the motorcycle is similar to making three pieces of toast toasted on both sides with a toaster that can only toast two pieces one-sidedly at any one time.
– h34
Jan 10, 2015 at 14:54