Rates and Work Answers
1.
(C).
If Sue completed exactly one more lap than Rob, she ran 10 more
miles than Rob. If Rob ran
d
miles, then Sue ran
d
+ 10 miles. Rob and Sue
began running at the same time, so they ran for the same amount of time. Let
t
represent the time they spent running. Fill out a chart for Rob and Sue, using
the formula Distance = Rate × Time (D = RT):
There are two equations:
d
= 6
t d
+ 10 = 8
t
Substitute 6
t
for
d
in the second equation and then solve for
t
:
6
t
+ 10 = 8
t
10 = 2
t
5 =
t
2.
(D).
To calculate Svetlana’s speed during the second half of the race, first
calculate how long it took her to run the first half of the race. Svetlana ran the
first 5 kilometers at a constant rate of 12 kilometers per hour. These values
can be used in the
D
=
RT
formula:
Svetlana’s time for the first part of the race is
hours, or 25 minutes.
She completed the entire 10-kilometer race in 55 minutes, so she ran the last 5
kilometers in 55 – 25 = 30 minutes, or 0.5 hours. Now create another chart to
find the rate at which she ran the last 5 kilometers:
5 = 0.5
r
10 =
r
Svetlana ran the second half of the race at a speed of 10 kilometers per hour.
3.
(E).
The question asks for the amount of time in hours, convert the work
rates from gallons per minute to gallons per hour. First, calculate the rate of
the standard machine:
Since the deluxe machine’s rate is twice the standard machine’s rate, the
deluxe machine can fill 15 × 2 = 30 gallons of paint per hour. Together, the
machines can fill 15 + 30 = 45 gallons of paint per hour. Now apply the
formula for work,
W
=
RT
:
135 = 45 ×
T
3 =
T
4.
(B).
Use two separate lines in a
W
=
RT
chart, one for Wendy and one for
Miguel, to calculate their respective rates. Building 1 birdhouse equals doing
1 unit of work:
Thus, Wendy’s rate is
birdhouses per hour, and Miguel’s rate is
birdhouses per hour. Since Wendy and Miguel are working together, add their
rates:
Now solve for
t
by first combining the fractions:
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