Taking the Train

May 23, 2016

Susan and Meaghan decide to meet at their favorite diner located near the Townsend Station. Susan leaves the Birchwood Station at 7:15 p.m. headed west on a train traveling 55 mi/h. Meaghan leaves the Meadowland Station at 7:30 p.m. headed east on a train traveling 70 mi/h. The two trains travel on parallel tracks and the distance between the Birchwood and Meadowland stations is 50 miles. If the girls get to the Townsend Station at the same time, at what time did their trains arrive? Express your answer as a time to the nearest minute.


Susan takes the train to work every day from Main Street Station to City Center Station. There are two trains she can take, the blue train and the yellow train. The arrival times for the yellow and blue trains are the same each day. The time between two blue trains is 20 minutes and the time between two yellow trains is also 20 minutes. Susan always arrives to the platform between 8 a.m. and 9 a.m. each day. She arrives at all times in this 1-hour window at equal frequency and gets on the first train that arrives to the station. She finds that she takes the blue train 3 times as often as the yellow train. What is the length of the interval in minutes between when a blue train arrives to the station and when a yellow train arrives?


Every day, Susan’s husband drives from their home to pick her up from the Main Street Station when she arrives at 6 p.m. He then drives them both home. Her husband takes the same route and drives the same speed each day. One day, Susan catches an earlier train and arrives at the Main Street Station at 5 p.m. She begins walking home along the same route her husband drives and meets him along the way. She gets in the car and they arrive home 10 minutes earlier than usual. How long did Susan walk for?