School-Safe Puzzle Games

Identical Cars

race car math puzzle

Imagine earth lost all it’s water, and the surface was evenly smooth. Two identical cars at the equator start traveling around the world in opposite directions. The cars start together, run at exactly the same speed, and are on different roads.

Which car will wear out its wheels first?

Will reveal submitted answers below next week!

UPDATE: the cars are traveling east/west, not north/south

8 Comments to “Identical Cars”

  1. Obiwan | Profile

    Does direction matter (N/S vs. E/W)?

  2. joe | Profile

    If we assume the cars will travel along the equator and that the drivers have enough water to live on, on this new harsh Earth, then the only thing I can think of is the fact that the car travelling West will spend more time in daylight, and therefore more sun and more heat. And this causes more tire wear.
    Why does it spend more time in daylight? Well say the Earth rotates at about 1000mph along the equator, if the car also travelled West at that speed it would be constantly in the sun. It probably won´t travel that fast but any fraction of it will still mean it spends more time in the hotter tire wearing part of the day. The other car will spend relatively more time in the cooler nights.

  3. andy75043 | Profile

    There’s not really enough information for a good answer. Currently existing production cars will spend as much time in daylight as dark, so sunlight will average out and not be a factor. On the other hand, if we postulate 1000 mph cars, this isn’t true, and the answer depends on whether or not the westbound car is always in sunlight; if so, the warmer roads will wear out the rubber tires faster.

    The other factor that might might make a difference is prevailing winds which, in the real world, are mostly west to east and would make the westbound car work harder (and therefore wear out its tires faster). But would that still be true on a smooth ocean-free Earth? I doubt that we know.

  4. andy75043 | Profile

    In re: my previous comment, I made a mistake. At the equator, where our (fictional) cars are, the prevailing winds are the trade winds out of the east, which would help the westbound car and make the eastbound one wear out its tires faster.

    Still, my previous comment stands. We don’t know what the prevailing winds would be on a smooth ocean-free world, and so we don’t know enough to answer the question.

  5. Obiwan | Profile

    Seems like too many potential variables unless there is a trick answer…
    1. Is there significant to “and are on different roads”? I assume not, but it is a
    curious statement.
    2. Are we to assume the “new earth” is a perfect sphere?
    3. Weather variations are gone because oceans are gone?
    4. Variables to think about:
    a) Miniscule differences in downward forces related to travel with versus against
    direction of earth rotation?
    b) Relationship to sun–tilted axis of rotation leading to more or less sun exposure, change in tire pressure related to more sunlight–>less wear in the car that has higher average tire pressures?
    c) Greater reduction in gravitation pull related to moon’s influence?

    This is probably an easy question for a geophysicist…

  6. RK | Founder | Profile

    The official answer I had relates to what Obiwan says in 4a: more friction related wear in the car traveling against the direction of earth rotation (more downward force).

    Joe, Andy,and Obiwan however, raise other variables that could play potentially a more important role!

  7. andy75043 | Profile

    Obiwan, the point of having different roads is that they won’t have a head-on collision half way around. I don’t think sphericity would matter, since both cars would have essentially the same handicap on average. I like your point about tidal forces, though; having one of the cars stay under the moon would definitely be both feasible and significant.

  8. seanogary | Profile

    The one coming from the east will wear out its tires first due to the earths rotation.

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