Problem number 29. Alex drives from point A to point B, then immediately returns to A. Bob drives from point B to point A, then immediately returns to B. They travel on the same road, start at the same time, and each travel at a constant speed. Alex's speed is three times Bob's speed. They pass each other for the first time 15 minutes after the start. How long after the start will they pass each other for the second time? So if we draw a diagram of the situation, let's label the first meeting as M, and the second meeting as N. Now, we can notice that in the first part of the trip, when they both reached for the first time, Alex is three times as fast as Bob. So from the first meeting, AM has to be equal to three times MB, since we know that Alex is three times as fast as Bob, and they both took the same time to reach the first meeting point. And that means that AM is three times MB. We also know that it took 15 minutes for Bob to travel that distance, MB, since that first meeting took place 15 minutes after the start. Now let's look at the second part of their journey, from M to N. Alex takes the path MB, BM, MN. He goes back and forth. But Bob only travels the distance MN. And we know by the same logic, since Alex is three times as fast, he will travel three times the distance Bob does. So that means that MB plus BM plus MN, which is the distance Alex travels, is three times MN, which MN is just the distance Bob travels in the second part. And so if we rewrite this, we get 2MB equals 2MN by subtracting MN from both sides, and dividing by two tells us that MB equals MN. And now notice that it takes Bob 15 minutes to go MB from the first part. And we know that MB equals to MN, so it must take 15 more minutes to go to the second meeting part, because that is how long it took to the first meeting part, and we know MB equals MN. So that means that to get to the first meeting point, it took 15 minutes, and to get to the second meeting point, 15 more minutes. So the total time it takes is 15 plus 15 equals 30 minutes. And that's the total time after the start, when they meet each other for the second time. The answer is C, 30 minutes.

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Bob

speed

meeting

distance