1.
Word Problems in 1 variable:
Part 8 (Uniform Motion)
Online Tutorial Series
July 2014

2.
Definitions
• Uniform Motion – Speed is the same all
throughout the trip.
• Distance = (Speed)*(Time)
• 3 Cases of Uniform Motion Problems:
– Moving Towards Each Other
– Moving Away From Each Other
– Chase

3.
Sample Problem
Case 1: Moving Towards Each Other
Two trains travel towards each other. If their
initial distance is 2800m, and reaches each
other after 40s. Find their speeds if the first
one is 10m/s faster?

4.
Solution
R: Let x be the speed of the slower train
x+10 be the speed of the faster train
E: time*speed = distance
40(x+10) + 40(x) = 2800
S: 40x + 400 + 40x = 2800
80x + 400 = 2800
80x = 2400; x=30, x+10=40
I: The first train’s speed is 40m/s, and 30/s for the
second.

5.
Sample Problem
Case 2: Moving Away From Each Other
Two trucks, with the first one faster than the
second by 20kph travels away from each
other. Find their speeds if after 15 hours, they
are 1500km apart?

6.
Solution
R: Let x be the speed of the slower truck
x+20 be the speed of the faster truck
E: time*speed = distance
15(x+20) + 15(x) = 1500
S: 15x + 300 + 15x = 1500
30x + 300 = 1500
30x = 1200; x=40, x+20=60
I: The two trucks travel at speeds 40 and 60kph.

7.
Sample Problem
Case 3: Chase
A truck leave a toll gate at 5pm, with speed of
50kph. If a car leaves the same toll gate at
7pm, but with speed of 70kph, what time will
the car meet the truck?

8.
Solution
R: If the truck travelled at 5pm, then no matter
how much in (t) hours the car travels, he travel
(t+2) hours
t -> time travelled by car
t+2 -> time travelled by truck
E: When they meet, they should have covered
the same distance
50 (t+2) = 70 (t)

9.
Solution
… 50 (t+2) = 70 (t)
50t + 100 = 70t
100 = 20t
t=5hrs, or 5 hours after the car left
or t+2=7hrs after the truck left
I: They will meet at 12mn.