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Interesting Math Problem

Interesting Math Problem Solution - 3 November

Alex and Martin are planning on a vacation. Alex says, "It will be better if we take the train to the hotel. We will reach faster."
To this, Martin says, "No. You are wrong. The train stops at halfway to the hotel and then we will have to walk the rest of the way. We should take the bikes to the hotel directly."
Alex says, "You are wrong."

Now, Alex takes the train while Martin takes the bike. The train travels with four times the speed of bike. The bike travels at twice the speed of walking.

Who do you think will reach the hotel first?

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Solution
Martin

S = total distance to the hotel.
V = walking speed.
2V = bike speed.
8V = train speed.
A = time taken by Alex
M = time taken by Martin

A = (S/2)/8V + (S/2)/V = S/16V + S/2V
M = S/2V

Now if you notice, A exceeds M by S/16V. Therefore, Martin will reach the hotel first.