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Distance = Rate  Time
D = rt
Algebra 2
Section 2.6
Motion Problems
1. A passenger train and a freight train start toward each other at the
same time from towns 870 km apart. The passenger train travels
80 km/hr and the freight train travels 65 km/hr. In how many hours
will they meet?
65 km/hr
80 km/hr
870 km
distance
80t
passenger
65t
freight
rate
80
65
80t + 65t = 870
145t = 870
t = 6 hrs
time
t
t (left at same time)
(combined distances = 870)
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2. A ship left port at 2:00 P.M. and traveled at 30 km/hr. At 6:00 P.M.,
a helicopter left the same port and flew at 120 km/hr in the same
direction as the ship. At what time did the helicopter reach the ship?
120 km/hr
6:00 pm
30t = 120t – 480
set distances equal to each other
30 km/hr
2:00 pm
distance
ship
30t
helicopter 120(t - 4)
120t - 480
rate
30
120
time
t
t–4
-90t = - 480
t = 5.333 {ship}
= 5 hrs 20 min
+
2:00 pm {ship’s time}
= 7:20 pm
{4 hr difference}
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3. Two cars start from the same point at the same time but travel in
opposite directions. One car averages 80 km/hr and the other averages
70 km/hr. In how many hours will they be 600 km apart?
80 km/hr
70 km/hr
600 km apart
one car
other car
distance
80t
70t
rate
80
70
time
t
t (left at same time)
80t + 70t = 600
150t = 600
t=4
(combined distances = 600)
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4. At 7:00 A.M., an armored van left city A and traveled at 70km/hr
toward city B. At 11:00 A.M. a helicopter, headed toward the van,
left city B and traveled at 110 km/hr. At approximately what time
did the helicopter reach the van if the cities are 550 km apart?
70km/hr
11:00 am
110 km/hr
7:00 am
550 km
distance
van
70t
helicopter 110(t - 4)
110t - 440
rate
70
110
time
t
t-4
70t + 110t – 440 = 550
180t = 990
t = 5.5hrs {van time}
+ 7:00 am
12:30 p.m.
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Solve each problem.
Algebra 2
Section 2.6
Assignment
1.) Two hockey players start toward each other at the same time from opposite ends
of an ice rink that is 60m long. In how many seconds will they meet if one player
skates at a rate of 9.5 m/s and the other skates at a rate of 10.5 m/s?
2.) John began the marathon run at 8:30 A.M. and averaged 12 km/hr. Mary began at 9:00 A.M.
and averaged 14 km/hr. At what time did Mary pass John on the marathon course?
3.) From a dock in a river, Cindy swam downstream at 4.4 m/s while George swam upstream
at 2.8 m/s. In how many seconds were they 108 m apart?
4.) One bus left the city at 2:00 P.M. and averaged 75 km/hr. Another bus, traveling in the
opposite direction, left the city at 5:00 P.M. and averaged 85 km/hr. At what time were the
buses 705 km apart?
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