### Section 8.3 - Problem Solving

```Name _______________________________________ Date __________________ Class __________________
LESSON
8-3
Problem Solving
Vicki and Lorena motor downstream at about 6 knots (nautical miles
per hour) in their boat. The return trip is against the current, and they
can motor at only about 3 knots.
1. Vicki wants to find the average speed for the entire trip.
a. Write an expression for the time it takes to travel downstream plus the time it takes for
the return trip if the distance in each direction is d.
b. What is the total distance they travel downstream and upstream in terms of d?
c. Write an expression for their average speed using the expressions for the total time
and the total distance.
d. Vicki says that the average speed is 4 knots. Lorena says that the average speed is 4.5
knots. Explain who is correct and why.
2. If they delay the return trip until the current changes direction, they can motor back at 4
knots. What is the average speed for the entire trip under these conditions?
Name _______________________________________ Date __________________ Class __________________
Zak runs at an average speed of 7.0 miles per hour during the first half of a race and an
average speed of 5.5 miles per hour during the second half of the race. Choose the letter
3. Which expression gives Zak’s average speed for the entire race?
A
C
 7  5.5 
2
 38.5  d
 7  5.5 
B
D
12.5  7  5.5  d
2
2  38.5  d
 7  5.5  d
4. If Zak runs the race in 1.25 hours, what is the length of the race in miles?
A 3.85
B 6.25
C 7.7
D 12.5
5. In a later race, Zak increased his average speed during the second half of the race to 6.0
miles per hour. What is his average speed for this race in miles per hour?
A 6.42
B 6.46
C 6.52
D 6.56
6. It took Zak 1.6 hours to run this later race. What is the length of this race in miles?
A 5.17
B 7.28
C 9.55
D 10.34
```