Question

Two trains are on the same track between San Francisco and New York. One train leaves San Francisco, heading east, at 8AM PDT on a Tuesday, and goes 45[kph] for 2 hours, and then speeds up to 95[kph]. Another train leaves New York, heading west, at 9AM CST on the same Tuesday, going 35[mph] for 100 miles, and then speeds up to 80[mph]. The train going west uses a steam locomotive, and the train going east uses a diesel. Assume that there are 2905 miles between San Francisco and New York, going through Des Moines and Salt Lake City.When will the trains meet?

Answer 1

The two trains will meet at a point when the train from New York has travelled a distance of 1678.57 miles in 22.589 hours.

Explanation:

We will first convert km to miles. We know that 8km = 5 miles ( approx). Therefore 45 kph = 28.125 mph and 95kph = 59.735mph. Also, we know that CST is ahead of PDT by 2 hours. Thus if the first train ( train B) starts from San Francisco at 8 AM PDT or 10 AM CST, and the second train ( train A) starts from New York at 9 AM , CST on the same day.

Suppose that the train A and B meet at a point after Train A has travelled for x hours. The train B would have travelled for x - 1 hours. The distance covered by train B in x - 1 hours is as under.

2 * ( 28.125) +( x -3) ( 59.735). Also, the distance covered by train A in x hours is as under.

Train A will cover 100 miles in 100/35 hrs i.e in 2.857 hrs. It has to travel further for x - 2.857 hrs more. Thus, the distance travelled by train A in x hours is 100 + (x - 2.857)80. Since the total distance covered by the two trains is 2905 miles., we have the following equation:

2 * ( 28.125) +( x -3) ( 59.735). + 100 + (x - 2.857)80 = 2905

or, 56.25 + 59.735x - 179.205 + 100 + 80 x - 228.56 = 2905

or, 139.735 x = 2905 + 251.515 =3156.515 or, x = 22.589 hors = 22 hours, 35 minutes, 21 second approximately.

The distance travelled by train A in this time is 100 + (x - 2.857)80 = 100 + ( 22.589 - 2.857)80 = 1678.57 miles

Thus the two trains will meet at a point when the train from New York has travelled a distance of 1678.57 miles in 22.589 hours.