Answer:
1+1
Step-by-step explanation:
1+1
1+1
1+1
1+1=2
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EXAMPLE: SOLVING AN APPLICATION USING A FORMULA
It takes Andrew 30 minutes to drive to work in the morning. He drives home using the same route, but it takes 10 minutes longer, and he averages 10 mi/h less than in the morning. How far does Andrew drive to work?
Show Show Solution
This is a distance problem, so we can use the formula
d
=
r
t
, where distance equals rate multiplied by time. Note that when rate is given in mi/h, time must be expressed in hours. Consistent units of measurement are key to obtaining a correct solution.
First, we identify the known and unknown quantities. Andrew’s morning drive to work takes 30 min, or
1
2
h at rate
r
. His drive home takes 40 min, or
2
3
h, and his speed averages 10 mi/h less than the morning drive. Both trips cover distance
d
. A table, such as the one below, is often helpful for keeping track of information in these types of problems.
d
r
t
To Work
d
r
1
2
To Home
d
r
−
10
2
3
Write two equations, one for each trip.
d
=
r
(
1
2
)
To work
d
=
(
r
−
10
)
(
2
3
)
To home
As both equations equal the same distance, we set them equal to each other and solve for r.
r
(
1
2
)
=
(
r
−
10
)
(
2
3
)
1
2
r
=
2
3
r
−
20
3
1
2
r
−
2
3
r
=
−
20
3
−
1
6
r
=
−
20
3
r
=
−
20
3
(
−
6
)
r
=
40
We have solved for the rate of speed to work, 40 mph. Substituting 40 into the rate on the return trip yields 30 mi/h. Now we can answer the question. Substitute the rate back into either equation and solve for d.
d
=
40
(
1
2
)
=
20
The distance between home and work is 20 mi.
Analysis of the Solution
Note that we could have cleared the fractions in the equation by multiplying both sides of the equation by the LCD to solve for
r
.
r
(
1
2
)
=
(
r
−
10
)
(
2
3
)
6
×
r
(
1
2
)
=
6
×
(
r
−
10
)
(
2
3
)
3
r
=
4
(
r
−
10
)
3
r
=
4
r
−
40
−
r
=
−
40
r
=
40
