One train travels the distance between stations in 26 minutes and the other in 39 minutes

| January 10, 2021 | education

One train travels the distance between stations in 26 minutes and the other in 39 minutes, after what time they will meet if they go out at the same time towards each other.

We denote by S the distance between stations, the speed of the first train by v1, and the speed of the second train by v2.
According to the condition of the problem, the first train covers the distance between stations in 26 minutes, therefore, the following relation is true:
S / v1 = 26.
It is also known that the second train covers the distance between stations in 39 minutes, therefore, the following relationship is true:
S / v2 = 39.
If two trains leave towards each other, then they will meet in S / (v1 + v2) minutes. Let’s define the meaning of this expression:
S / (v1 + v2) = 1 / ((v1 + v2) / S) = 1 / (v1 / S + v2 / S).
Substituting the values ​​v1 / S = 1/26 and v2 / S = 1/39 into the resulting expression, we get:
1 / (v1 / S + v2 / S) = 1 / (1/26 + 1/39) = 1 / (5/78) = 78/5 = 15.6 min = 15 min 36 sec.
Answer: if two trains leave towards each other, then they will meet in 15 minutes and 36 seconds.



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