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Need help with simple math problem. (lemmy.ml)

submitted 5 months ago by Donatello@lemmy.ml to c/math@lemmy.ml

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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.

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[–] meant2live218@lemmy.world 6 points 5 months ago* (last edited 5 months 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.