# Defining Word Problems by byrnetown67

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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?
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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.
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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)

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