Algebra Demystified 2nd Ed

292 algebra De mystif ieD

2. The distance between the cars is decreasing at the rate of 65 + 55 =
   120 mph. Let t represent the number of hours the cars have traveled
   since entering the highway.

120 270

270

120

241

t

t

t

=

=

=

The cars will meet after 214 hours or 2 hours 15 minutes.

3. The distance between the joggers is decreasing at the rate of 6 + 9 =
   15 mph. Let t represent the number of the hours they are jogging.
   15 9
   9
   15
   3
   5

t

t

t

=

=

=

The joggers will meet after^35 of an hour or^60 () 53  = ^36 minutes.

Some distance problems involve the complication of the two bodies starting

at different times. For these, we compute the head start of the first one and let

t represent the time they are both moving (which is the same as the amount of

time the second is moving). We then subtract the head start from the distance

in question then proceed as if they started at the same time.

EXAMPLE

A car driving eastbound passes through an intersection at 6:00 at the rate

of 30 mph. Another car driving westbound passes through the same inter-

section ten minutes later at the rate of 35 mph. When will the cars be

18 miles apart?

The eastbound driver has a 10-minute head start. In 10 minutes (^1060 hours),

that driver has traveled (^30) ()^1060  =  5 miles. So when the westbound driver
passes the intersection, there is already 5 miles between them, so the ques-
tion is now “How long will it take for there to be 18 – 5 = 13 miles between
two bodies moving away from each other at the rate of 30 + 35 = 65 mph?”
EXAMPLE
A car driving eastbound passes through an intersection at 6:00 at the rate