Q. Chandra Prakash was travelling in Ahmedabad Express. While he was sleeping, Jamnagar Mail from opposite direction crossed his train at a great speed. The noise made by the Mail train woke Chandra Prakash. He sat up still half-asleep. He began to look around. His co-passengers were talking. Chandra also listened to them.
“Shyam, the Jamnagar Mail was going at a great speed, don’t you think so?”
“Indeed, Dev Kaka! It crossed our train just in a matter of seconds. What do you think the speed was?” Shyam asked.
Dev Kaka replied, “Yes, the speed was considerably great. But our train too is running at much speed. Ahmedabad Express, as you know, is less than one thousand feet but is longer than the Jamnagar Mail by 150 feet. Besides, the mail had diesel engine.”
“Yes uncle, but I couldn’t find out the speed.”
Chandra Prakash who was listening to this conversation intervened and said that if he knew the time taken by these trains to cross each other and their total length, he would be able to tell the speed of the Jamnagar Mail.
Dev Kaka offered the following details: “The average speed of the Jamnagar Mail is so much more than Express that it could have crossed the Express in one minute. Both the trains were running at a speed that was in whole numbers in miles. If they came from opposite directions they would pass each other in 10 seconds. I have never measured their total length, but definitely it is not less than 550 yards.”
Now tell the average speed and length of both the trains.
A. Length of Jamnagar Mail – 800 feet. Average speed – 70 mph or 115 km. Length of Ahmedabad Express – 960 feet.
Average speed – 50 mph. (or 80 km).
Note:
Both trains are less than 1000 feet in length. The total length of both trains is more than 1550 feet and less than 1840 feet.
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