Algebra Demystified 2nd Ed

442 algebra De mystif ieD

Round-trip Problems

In the following problems, people are making a round trip. The average speed

in each direction is different, and the total trip time is given. The equation we

want to solve is

Time to destination + Time on return trip = Total trip time

To get the time to and from the destination, we again use t D

r

= , from D = rt.

The equation that we want to solve becomes

Distance

Rate todestination

Distance

Rateon ret

+

uurntrip

=Totaltriptime

EXAMPLE

A jogger jogged seven miles to a park then jogged home. He jogged 1 mph

faster to the park than he jogged on the way home. The round trip took

2 hours 34 minutes. How fast did he jog to the park?

Let r represent the jogger’s average speed on the way home. He jogged

1 mph faster to the park, so r + 1 represents his average speed to the

park. The distance to the park is 7 miles, so D = 7.

Time to the park + Time home = 2 hours 34 minutes

The time to the park is represented by t

r

= 

+ 

7

1

. The time home is represented
by t
r

 = ^7. The round trip is 2 hours 34 minutes = ^3460 = ^1730 = 22 3077 hours.

The equation to solve becomes^7

1

777

rr 30

+ 

+  = .

The LCD is 30r(r + 1).

30 1 7

1

30 17 30 177

30

210 210

rr

r

rr

r

rr

rr

() () ()

(

+

+

++=+

++ 11771

210 210 210 77 77

420 210 77

2

2

)(=+)

++=+

+=

rr

rr rr

rr++

=−−

77

0772 343 210

r

rr

EXAMPLE

A jogger jogged seven miles to a park then jogged home. He jogged 1 mph

faster to the park than he jogged on the way home. The round trip took

2 hours 34 minutes. How fast did he jog to the park?

EXAMPLE

A jogger jogged seven miles to a park then jogged home. He jogged 1 mph