Hi,

I found online a nice (and seemed easy) math problem.

Rocket A travel from Mars to Earth in 200 days
Rocket B travel from Earth to Mars in 150 days, but take off 30 days later

When they cross each other, which one is the closet to the earth ?

So they give a “flat” answer, without giving any explanation on how they reach this conclusion.

What would be your simplest Mathematical solution for this ?

Thanks.

  • @meant2live218
    6•1 month ago

    Edit: I didn’t read the entirety of the problem, but in any case, this should help you state almost anything regarding the simple math. Note that in actuality, I don’t think there would be a true meeting place due to orbital paths, but if you treat it as a linear “train” problem, this is how I would do it.

    This may not be the simplest, but here’s an easy way to just use lots of substitution and basic algebra.

    Let t = time in days to meet

    Let a = speed (not velocity) of rocket A

    Let b = speed (not velocity) of rocket B

    1 = 200 * a

    1 = 150 * b

    200a = 150b

    a = (3/4)b

    1 = (t * a) + (t - 30) * b

    Substitute for a

    1 = (3/4)bt + bt - 30b = (7/4)b - 30b

    Recall that 1 = 150 * b and set these equal

    150b = (7/4 * t - 30) b

    Divide by b

    150 = 1.75t - 30

    1.75t = 180

    t ~ 103 days

    At 103 days, the ships will meet, and since it’s over half the time it takes for rocket A to reach Earth, the meeting point will be closer to Earth.