Solving a Motion Problem (Motion in the Same Direction)
Jeff can bike to work in When he takes the bus, the trip takes If the bus trav-
els 20 mph faster than Jeff rides his bike, how far is it to his workplace?
Step 1 Readthe problem. We must find the distance between Jeff ’s home and his
workplace.
Step 2 Assign a variable.Although the problem asks for a distance, it is easier here
to let xbe Jeff ’s rate when he rides his bike to work. Then the rate of the bus
is
For the trip by bike,
For the trip by bus,
Summarize this information in a table.
d= rt= 1 x+ 202 #
1
4
=
1
4
1 x+ 202.
d= rt=x#
3
4
=
3
4
x.
x+ 20.
1
4 hr.
3
4 hr.
EXAMPLE 3
SECTION 2.4 Further Applications of Linear Equations 83
Rate Time Distance
Bike x
Bus
1
4 1 x+^202
1
x+ (^204)
3
4
(^3) x
4
Same
Step 3 Write an equation.The key to setting up the correct equation is to
understand that the distance in each case is the same. See FIGURE 7.
Home Workplace
FIGURE 7
The distance is the same
in each case.
Step 4 Solve. Multiply by 4.
Multiply;
Subtract x.
Divide by 2.
Step 5 State the answer.The required distance is
Step 6 Checkby finding the distance using
d=
1
4
1 x+ 202 =
1
4
110 + 202 =
30
4
=7.5 mi.
d=
3
4
x=
3
4
1102 =
30
4
= 7.5 mi.
x= 10
2 x= 20
3 x= x+ 20 1 x=x
4 a
3
4
xb = 4 a
1
4
b1x+ 202
3
4
x=
1
4
1 x+ 202
The same
result
NOW TRY
As in Example 3,the equation for a problem involving motion in the samedirec-
tion is usually of the following form.
one distanceother distance
NOW TRY
EXERCISE 3
Michael Good can drive to
work in hr. When he rides his
bicycle, it takes hours. If
his average rate while driving
to work is 30 mph faster than
his rate while bicycling to
work, determine the distance
that he lives from work.
(^1 12)
1
2
NOW TRY ANSWER
- 22.5 mi