Defining Word Problems by byrnetown67

VIEWS: 188 PAGES: 3

									Page 1 of 3


                            Defining Word Problems:
                           Motion in the Same Direction
                             Motion with Movement
                                  Worksheet 10

    Motion in the Same Direction
    FORMULAS:           Distance     = rate X time
                             D       = rt

    EXAMPLE. A helicopter leaves Central Airport and flies north at 180 mph. Twenty minutes
    later a plane leaves the airport and follows the helicopter at 330 mph. How long does it
    take the plane to overtake the helicopter?

                        STEP 1: Make a chart.

                                            Rate         X      Time            =     Distance
                   Helicopter              180                   t + 1/3             180(t+ 1/3)

                      Plane                330                       t                  330t

                        STEP 2: Let t       = the time the plane traveled
                                 (t + 1/3) = the time the helicopter traveled

                        STEP 3: Define an equation.
                                Distance of the helicopter = Distance of the plane

                                         330t = 180(t +1/3)
                        STEP 4: Solve.
                                         330t = 180t + 60
                                         150t = 60
                                            t = 2/5  time of plane

                        STEP 5 Check.


                  Distance of Helicopter  1/3(180) + 2/5 (180) = 132 miles
                  Distance of Plane      2/5(330) = 132 miles √
                        STEP 6: Write the answer in a full sentence.
                        The plane overtakes the helicopter in 2/5 hours, or 24 minutes.




        1. A small plane leaves an airport and flies north 250 mph. A jet leaves the airport 30
           minutes later and follows the small plane at 375 mph. How long does it take the jet to
           overtake the small plane?
Page 2 of 3

     2. A car started out from Memphis toward Little Rock at the rate of 60 km/h. A second
        car left from the same point 2 hours later and drove along the same route at 75 km/h.
        How long did it take the second car to overtake the first car?

     3. A tourist bus leaves Richmond at 1:00 P.M. for New York City. Exactly 24 minutes
        later, a truck sets out in the same direction. The tourist bus moves at a steady 60
        km/hour. The truck travels at 80 km/hour. How long did it take the truck to overtake
        the tourist bus?

     4. Exactly 20 minutes after Alex left home, his sister Alison set out to overtake him.
        Alex drove at 48 mph and Alison drove at 54 mph. How long did it take Alison to
        overtake Alex?

     5. The McLeons drove from their house to Kayton at 75 km/hour. When they returned,
        the traffic was heavier and they drove at 50 km/hour. If it took them1 hour longer to
        return to go, how long did it take them to drive home?

     6. It takes a plane 1 hour less to fly from San Diego to New Orleans at 600 km/hour
        than it does to return at 450 km/h. How far apart are the two cities?

     7. A small plane leaves an airport and flies north 180 mph. A jet leaves the airport 20
        minutes later and follows the small plane at 330 mph. How long does it take the jet to
        overtake the small plane?
     8. A car started out from Memphis toward Little Rock at the rate of 48 km/h. A second
        car left from the same point 2 hours later and drove along the same route at 60 km/h.
        How long did it take the second car to overtake the first car?


     9. One car travels 50 miles per hour and another one travels 55 miles per hour. If they
        start from the same place and travel in the same direction, after how many hours will
        the faster car be 35 miles ahead of the slower car?

     10. One car travels 62 miles per hour and another one travels 48 miles per hour. If they
         start from the same place and travel in the same direction, after how many hours will
         the faster car be 42 miles ahead of the slower car?

     11. One car travels 45 miles per hour and another one travels 52 miles per hour. If they
         start from the same place and travel in the same direction, after how many hours will
         the faster car be 42 miles ahead of the slower car?

     12. One car travels 56 miles per hour and another one travels 31 miles per hour. If they
         start from the same place and travel in the same direction, after how many hours will
         the faster car be 75 miles ahead of the slower car?

     13. Two freight trains started at the same time from towns 564 miles apart and met in six
         hours. The average rate of one train was 14 miles per hour faster than that of the
         other train. Find the rate of each train.
Page 3 of 3


    14. Two passenger trains started at the same time from towns 608 miles apart and met
       in 4 hours. The rate of one train was 8 miles per hour slower than that of the other.
       Find the rate of each train.

    15. Jose left Westcliff on his bicycle riding at an average of 8 miles per hour five hours
        before his father left by automobile. The father overtook Jose in exactly one hour. At
        what average rate was Jose’s father traveling?

    16. Lisa left camp on her bicycle at noon and rode at an average rate of 10 miles per
        hour. Morton left camp in his van at 1:30 P.M. and overtook Lisa in 30 minutes. At
        what average rate was he traveling in the van?

    17. Two freight trains started at the same time from towns 448 miles apart and met in 8
        hours. The average rate of one train was 19 miles per hour faster than that of the
        other train. Find the rate of each train.

    18. Two passenger trains started at the same time from towns 288 miles apart and met in
        3 hours. The rate of one train was 6 miles per hour slower than that of the other.
        Find the rate of each train.




Algebra- Structure and Method, Pg. 169-170
*Dale Seymour Publications, Developing Skills in Algebra, Book A, pg 97,98
(ALGEBRA 2006-2007 DWPDistance(Same) 10.doc)

								
To top