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This problem trains for: SAT-I, AMC-8, GMAT.
A loop-shaped bus line has equidistant stops. On average, the waiting time at a stop between two consecutive buses is 6 minutes. If the number of buses is increased by 25%, what is the new interval of time between two consecutive arrivals of a bus at some stop?
By dividing the length of the loop l by the total number of buses b we find out the length of line that spaces out two consecutive (adjacent) buses. This length is proportional to the average speed of the bus v and the time t it takes for it to cover it:
If the number of buses increases by 25% then this length becomes:
where x is the time it takes a bus to cover the new length.
Dividing the two previous equalities by one another:
4.8 minutes is 4 min 48 s which is not an answer choice. By converting this time to seconds we find that 4.8 minutes is 288 s.
Note that this solution is correct only under certain assumptions regarding the system it models. For example, whatever the values of the line length and number of buses, the average speed should have a reasonable value. Also, the length of the bus is considered small (negligible) with respect to the distance that separates two consecutive buses.