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The rate of the passenger train is 45 miles per hour

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Unformatted text preview: se, d1 + d2 = total distance covered. B. Motion in the same direction This type of problem is sometimes referred to as a “catch up” problem. Usually two objects leave the same place at different times and at different rates, but the one that leaves later “catches up” to the one that leaves earlier. In such cases the two distances must be equal. If one is still ahead of the other, then an equation must be written expressing this fact. C. Round trip In this type of problem, the rate going is different from the rate returning. The times are also different. But if we go somewhere and then return to the starting point, the distances must be equal. To solve any type of motion problem, it is helpful to organize the information in a chart with columns for rate, time, and distance. A separate line should be used for each moving object. Be very careful of units used. If the rate is given in miles per hour, the time must be in hours and the distance will be in miles. Example: A passenger train and a freight train leave at 10:30 A.M. from stations that are 405 miles apart and travel toward each other. The rate of the passenger train is 45 miles per hour faster than that of the freight train. If they pass each other at 1:30 P.M., how fast was the passenger train traveling? Solution: Notice that each train traveled exactly 3 hours. Rate Passenger Freight 3x + 135 + 3x = 405 6 x = 270 x = 45 · Time 3 3 = Distance 3 x + 135 3x x + 45 x The rate of the passenger train was 90 m.p.h. Problem Solving in Algebra 183 Example: Susie left her home at 11 A.M., traveling along Route 1 at 30 miles per hour. At 1 P.M., her brother Richard left home and started after her on the same road at 45 miles per hour. At what time did Richard catch up to Susie? Solution: Rate Susie Richard 30 45 · Time x x–2 = Distance 30x 45x – 90 Since Richard left 2 hours later than Susie, he traveled for x – 2 hours, while Susie traveled for x hours. Notice that we do not fill in 11 and 1 in the time column, as these are times on the clock and not actual hours traveled. Since Ric...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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