Answer to Question #29046 in Algebra for diya

Question

Taxies leave station x for station y every 10 minutes. Simultaneously taxies leave station y for station x every 10 minutes. The taxies move with the same constant speed . The time taken to reach y from x or y to x is 2 hours . How many taxies can cross a taxi from station x.

Answer 1

Let the moment of time when this particular taxi (call it M)leaves from station X, be t = 0. We track back to t = -120 min, when a taxi from station Yleft, and now it is arriving at X, so this is the 1st one to cross our M. As the M moves along the road, it crosses taxis every 5 minutes. At the center of the distance it meets the taxi that left Yat the same moment as it did leave X, t = 0.
By that time it is the 13th taxi to cross. When M arrives finally at destination Y, there is also ataxi to depart from Y at that very moment, making it the last taxi to meet. The total number is (120min)/(10 min) * 2 + 1 = 12*2 + 1 = 25.

Answer: 25 taxis