1. SAT PREP
UPSTREAM / DOWNSTREAM
& MOTION
Rita Korsunsky

2. Example 1
A frog swims 8 miles downstream in 2 hours. He returns upstream in 14 hours. How fast does the frog swim in still water?
Solution:
Upstream
Downstream
D: 8
R: x-c
T: 14
R: x+c
T: 2
Still water rate: x
Current rate: c

3. Example 2
A steamboat made a round trip between two ports 24 miles apart. If the average speed for the entire trip was 4.8 mph and the steamboat took 4.5 hours to travel downstream, how many hours did it take to go upstream?
Solution:
Downstream
D: 24
T: 4.5
Upstream T:

4. Example 3
A passenger train and a freight train leave at 10:30AM from stations 405 mi apart and travel toward each other. The passenger train is 45 mph faster than the freight train. If they pass each other at 1:30PM, how fast was the passenger train traveling?
Solution:
Passenger
D: 3x+135
R: x+45
T: 3
Freight
D: 3x
R: x

5. Example 4
Car A left a city at 2:00PM and traveled at an average speed of 40 miles per hour. Car B left at 4:00PM, traveled the same route and overtook the first car at 9:00PM. What was the average speed of Car B?
Solution:
Car A
D: x
R: 40
T: 7
Car B R:
T: 5

6. Example 5
Susie left home at 11AM traveling at 30 mph. At 1PM, her brother Richard left home and started on the same road at 45 mph. When did he catch up to her?
Solution:
Susie
D: 30x
R: 30
T: x
Richard
D: 45x-90 R: 45 T: x-2
He caught up to her at
6 hours after 11AM is 5PM.

7. Example 6
Roberto travels from his home to the beach at 30 mph. He returns at 50 mph. If the distance from his house to the beach is 10 miles, what is Roberto’s average speed for the round trip?
Solution:
Going
D: 10
R: 30 T:
Returning
R: 50