SOLUTION: A train leaves Union Station for Central Station, 216 km away, at 9 a.m. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train ha

Question 1033445: A train leaves Union Station for Central Station, 216 km away, at 9 a.m. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 a.m., and the first train at 10:30 a.m., they would still have met at noon. Find the speed of each train.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Use a time line instead of time points. Your trains seem described as traveling
in opposite directions and moving toward each other.
RT=D is a basic travel rates rule connecting RATE, TIME, DISTANCE.

VEHICLES        RATE      TIME      DISTANCE
---------------------------------------------
Case1
A                r        2+1
B                s         2
Total                                 216
---------------------------------------------
Case2
A                r        3/2
B                s        3
Total                                 216
---------------------------------------------

Time values can be found without putting them as variables. The two unknown variables
are FirstTrain at rate r and SecondTrain at rate s. Each situation uses time span of
three hours, but case 1 is when train number two travels less time; and case 2 is when
first train travels less time. Think and review the data table before continuing...

-----to continue, fill-in the distance expressions.

VEHICLES        RATE      TIME      DISTANCE
---------------------------------------------
Case1
A                r        2+1        r*3
B                s         2          s*2
Total                                 216
---------------------------------------------
Case2
A                r        3/2        r*(3/2)
B                s        3          s*3
Total                                 216
---------------------------------------------

Solve this system for r and s, the speeds of FirstTrain and SecondTrain.

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