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?

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.

Step-by-step 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.

sine

step-by-step explanation: