Mathematics

Mathematics

Problem

Two buses leave a depot together at 7:30 a.m. on different routes. Bus A returns to the depot every 24 minutes, while Bus B returns every 32 minutes. (i) After how much time will both buses arrive back at the depot together for the first time after 7:30 a.m.? (ii) By that time, how many trips will Bus A have completed? Select the correct option. a) 1 h 12 min; 3 trips1\ \text{h}\ 12\ \text{min};\ 3\ \text{trips} b) 0 h 56 min; 2 trips0\ \text{h}\ 56\ \text{min};\ 2\ \text{trips} c) 1 h 36 min; 4 trips1\ \text{h}\ 36\ \text{min};\ 4\ \text{trips} d) 1 h 36 min; 5 trips1\ \text{h}\ 36\ \text{min};\ 5\ \text{trips}
Intuitive explanation

This problem is about finding when two repeating events happen at the same time—a classic application of the least common multiple (LCM). Bus A and Bus B return on fixed schedules, so you need to find the smallest time interval that is a multiple of both 24 and 32 minutes. Once you have that, dividing by each bus's cycle time tells you how many complete trips each has made.

Intuitive explanation

This problem is about finding when two repeating events happen at the same time—a classic application of the least common multiple (LCM). Bus A and Bus B return on fixed schedules, so you need to find the smallest time interval that is a multiple of both 24 and 32 minutes. Once you have that, dividing by each bus's cycle time tells you how many complete trips each has made.

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