A train needs 4 hours to go from the first station to the second and the total travel time must be no more than 7 hours, then the train needs at most 3 hours to go from the second station to the third station.
The average speed can be obtained by the formula:
\(V_{\text{average}}=\dfrac{\text{total distance}}{\text{total time}}.\)
Let V be the train speed between first and second stations, then the distance between the first and the second stations is 4V miles.
Therefore,
- the total distance is 4V+120 (V>0);
- the total time is T≤7 hours.
Now
\(V_{\text{average}}=\dfrac{\text{4V+120}}{\text{T}}, \text{ where } T\le 7, V>0.\)
The slowest average speed will be when nominator is the smallest and denominator is the greatest. The greatest denominator could be T=7, then
\(V_{\text{average}}=\dfrac{\text{4V+120}}{7}=\dfrac{4V}{7}+17.14> 17.14\)
