Rate-Time-Distance
Problems
Algebra 1

Rate-Time-Distance Problems
•
An object is in
uniform motion
when
it moves without changing its
speed, or rate. These problems fall
into 3 categories: Motion in opposite
directions, Motion in the same
direction, & Round Trip. Each is
solved using a chart, a sketch, and
the distance formula
.
T
D
R
R
D
T
RT
D
or
or

Motion in the Same DirectionA helicopter leaves Central Airport and flies north at 180 mi/h. Twenty minutes later a plane leaves the airport and follows the helicopter at 330 mi/h. How long does it take the plane to overtake the helicopter.
⅓
)

Rate
Time
Distance
Helicopter
Plane
180
330
t +
⅓
t
180(t +
⅓
)
330t
When the plane overtakes the helicopter, the two
distances are equal.
3
1
180
330
t
t
60
180
330
t
t
60
150
t
min.
24
or
h
5
2
t

Officer Barbrady left his home at 2:15 PM and had driven 60 miles when he ran out of gas. He walked 2 miles to a gas station, where he arrived at 4:15 pm. If he drives 10 times as faster than he walks, how fast does he walk?
Distance
Rate
Time
Driving
Walking
r
10r
60
2
r
2
r
10
60

Set to Equal
15)
:
4
to
15
:
(2
2h
Walking
Time
Driving
Time
2
2
10
60
r
r
2
10
20
10
60
r
r
1
80
10
2
r
r
4
Office Barbrady walked at a rate of 4/mph
1
2
10
80
r
80
20
r