Due to an extremely unfortunate error involving a train that was behind schedule and a watch that may have been four minutes slow, there was a head-on collision of two trains in the town of Kipton in 1891. The plan was that the slow westbound passenger train, traveling at 8 miles per hour, would be able to get onto a siding in time to get out of the way of the fast eastbound mail train, traveling at 45 miles per hour. But it didn’t work out that way. (You can Google Kipton Train Wreck to find out the details.) Our concern here is with a fly. When the two trains were exactly 10 miles apart, the fly, sitting on the front of the westbound engine, flew down the tracks to the eastbound train at 60 miles per hour. When it got there, it turned around immediately and flew back to the westbound train, thence to the eastbound, thence to the westbound, back and forth, over and over, going a shorter distance each time. The question, of course, is how far did the fly fly before being crushed between the two engines as they collided?
Quantitative Reasoning
Reservoir Running
Amy and Phyllis are standing at opposite points on a round pond on the path that circles the pond at its edge. At the same time, they start racing around the pond in opposite directions. They meet for the first time after Phyllis has traveled 100 yards, and they meet again 60 yards before Amy has completed her first lap. What is the circumference of the path around the pond?
Train in Tunnel
A freight train that is 1 mile long goes through a tunnel that is 2 miles long. If the train is traveling at 15 miles per hour, how long does it take it to pass completely through the tunnel?
Part 2: Generalize: the train is n miles long; the tunnel is m miles long, and the train is going r miles per hour. The answer this time will of course be a formula.
Train Roars Through Station
An express train roars through the train station, taking 5 seconds to pass a waiting passenger, and 19 seconds to clear the whole station. The platform is 280 meters long. How long is the train, and at what speed is it moving?
Daniel Boone, Plum Creek
Daniel Boone can paddle his canoe at 15 mph in still water. He is, however, paddling on Plum Creek, which rages along at 5 mph. He paddles downriver for a while, then turns around and paddles back upstream to his starting point. What is his average speed for the entire trip?
The Rocket Sled
Your science class is on a field trip to a rocket testing site. A rocket sled traveling 900 meters per second on a track passes the place where you are standing. Suddenly, 270 meters farther down the track the rocket explodes quite unexpectedly. If you hear the sound of the explosion 1.1 seconds after the sled passes by, you can calculate the speed of sound. So do it.
Huey, Dewey, Louie Numbers
Huey, Dewey, and Louie find that they must get from their home in Duckburg to a friend’s house in Possumtown, a distance of 52 km. Louie has a motorcycle, but it can manage only one passenger at a time in addition to the driver. This cycle can only go 20 kph at best. The three of them hit on a plan: Louie will take Huey part of the way, and then leave him to walk the rest of the way (at 5 kph). Then Louie will return to pick up Dewey, who has been walking all the while at 4 kph, and they will ride the rest of the way to Possumtown. They carried out their plan, which brought them all to their destination at exactly the same time. Now, can you figure out how many hours it took for the whole adventure?
Columbus to Cincinnati
At 12:00 noon, Lunis started driving from Columbus to Cincinnati at a steady 40 mph. Fifteen minutes later, at 12:15, Ethan started driving from Cincinnati to Columbus at a steady 50 mph. The two cars passed each other at a point midway between the two cities. Using this information, calculate the distance between Columbus and Cincinnati. (Is this distance correct?)
Driving to Atlanta
Manzy’s car, that he had in the 1980’s, had a 24-gallon gas tank. When he started driving one morning with a full tank, heading for Atlanta, the odometer read 3208 miles. He drove for most of the day, having stopped at lunch to buy 5 gallons of gas. The gas gauge said exactly � of a tank at the point where the odometer read exactly 3668. He still had 130 miles of driving to do to get to Atlanta. Back then, gas cost only $1.09 per gallon, and he had only $2.00 left on him and no credit cards. Did he make it into the city? (Give all details.)
Driving to See Grandmother
Kim drove 84 miles to see her grandmother. Nine miles of the trip were inside the city limits. Her average speed outside the city was 12 mph faster than inside the city. The whole trip took 3 hours. How fast did Kim go while inside the city?