Warm Up

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Warm Up
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Math 8H

• Problem Solving Day 2

Algebra 1 Glencoe McGraw-Hill JoAnn
Evans
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Two Types of rate time distance Problems

• d d d
• Distance distance total
• vehicle 1 vehicle 2 distance
• The two vehicles will either be
• starting at opposite ends and
• traveling toward each other
• -or-
• they will start at the same
• place and travel in opposite
• directions until they reach a
• given distance apart.

• d d
• distance of distance of
• vehicle 1 vehicle 2
• This is the catch up formula.
• The first vehicle will start, then
• the second vehicle will begin at
• a later time , traveling at a
• faster speed, until it catches up
• with the first vehicle.
• -or-
• It is the round trip formula.

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Example 1 d d total distance
Two trains left the same station at the same time
and traveled in opposite directions. The E train
averaged 130 km/h and the A trains speed was 110
km/h. In how many hours were they 480 km apart?
start
E train
A train
480 km apart
The problem gives the distance and the rates.
You need to find the time. Let t time
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Verbal Sentence E trains distance A
trains distance total distance d
d
d Remember d rt
rt rt
d Equation 130t
110t
480 Solution The trains were 480 km apart
in 2 hrs.
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Example 2 d d total distance
Two cars traveled in opposite directions from the
same starting point. The rate of one car was 20
km/h less than the rate of the other car. After
5 hours, the cars were 700 km apart. Find the
rate of each.
start
Faster Car
Slower car
700 km apart
The problem gives the distance and the time.
You need to find the rate. Let r
rate of faster car Let r 20
rate of slower car
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Verbal Sentence faster cars dist.
slower cars dist. total distance d
d d Remember d rt
rt rt
d Equation r5
(r-20)5 700 Solution The
faster car is 80 km/h and the slow is 60 km/h.
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Example 3 d d
Sam started out in his car traveling at 60 mph.
Two hours later, Jenny left from the same point.
She traveled along the same road at 75 mph.
After how many hours will she catch up with Sam?
Sams car
Point where Jenny caught up
start
Jennys car
The problem gives the rate. You need to
find the time. Let t Jennys time
Let t 2 Sams time (he started 2 hrs
earlier)
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Verbal Sentence Jennys distance
Sams distance d d
Remember d rt
rt rt Equation
75t 60(t
2) Solution It took Jenny 8 hours to catch
up with Sam.
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Example 4 d d
The Peterson family drove to the beach at 75
km/h. They returned later in heavy traffic,
slowed to 50 km/h. It took 1 hour longer to
return home than it did to get to the beach. How
long did it take to get home?
to the beach
return home
The problem gives the rate. You need to
find the time. Let t time to return home
Let t - 1 time it took to get to beach
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Verbal Sentence distance home
distance to beach Remember d rt
rt
rt Equation 50t
75(t 1) Solution It took 3
hours to return home.
d d