SOLUTION: A train running between two towns arrives at it's destination 10 mins late when it travels at a constant rate of 40 mph and 16 mins late when it travels at a constant rate of 30 mi

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Question 810315: A train running between two towns arrives at it's destination 10 mins late when it travels at a constant rate of 40 mph and 16 mins late when it travels at a constant rate of 30 miles per hour. What is the distance, in miles, between the two towns?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use t as target time length if the train were on-time. There are two speed conditions:

Speed__________________Time hours______________distance miles
40_____________________t%2B10%2F60_________________40%28t%2B1%2F6%29
30_____________________t%2B16%2F60_________________30%28t%2B4%2F15%29

The distance expressions in the table were both somewhat simplified, and based on Rate%2ATime=Distance. These distances are EQUAL, being between two given but unspecified same towns. We form this equation:

highlight%2840%28t%2B1%2F6%29=30%28t%2B4%2F15%29%29
Solve for t, the target time, and then use it to compute distance between the towns, using either distance expression.