Sat math Essentials

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P R O B L E M S O LV I N G
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1 6 0

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Unknown 
time for Boat 2, traveling 30 mph to go around the lake 
x
Known 
time for Boat 1, traveling 45 mph to go around the lake 
x
0.75
Then, use the formula (Rate)(Time) 
Distance to write an equation. The distance around the lake does not
change for either boat, so you can make the two expressions equal to each other:
(Boat 1 rate)(Boat 1 time) 
Distance around lake
(Boat 2 rate)(Boat 2 time) 
Distance around lake
Therefore:
(Boat 1 rate)(Boat 1 time) 
(Boat 2 rate)(Boat 2 time)
(45)(
x
0.75) 
(30)(
x
)
45
x
33.75 
30
x
45
x
33.75 
45
x
30
x
45
x
33
1
.
5
75
1
1
5
5
x
2.25 
x
2.25 
x
Remember:
x
represents the time it takes Boat 2 to travel around the lake. We need to plug it into the formula
to determine the distance around the lake:
(Rate)(Time) 
Distance
(Boat 2 Rate)(Boat 2 Time) 
Distance
(30)(2.25) 
Distance
67.5 
Distance
The distance around the lake is 67.5 miles.
Practice Question 
Priscilla rides her bike to school at an average speed of 8 miles per hour. She rides her bike home along the
same route at an average speed of 4 miles per hour. Priscilla rides a total of 3.2 miles round-trip. How
many hours does it take her to ride round-trip?
a.
0.2
b.
0.4
c.
0.6
d.
0.8
e.
2
Answer
c.
Let’s determine the time it takes Priscilla to complete each leg of the trip and then add the two times
together to get the answer. Let’s start with the trip from home to school:
Unknown 
time to ride from home to school 
x
Known 
rate from home to school 
8 mph
Known 
distance from home to school 
total distance round-trip 
2 
3.2 miles 
2 
1.6 miles
Then, use the formula (Rate)(Time) 
Distance to write an equation:
(Rate)(Time) 
Distance
8
x
1.6