When two bodies travel towards each other (from opposite directions) the rate at which the distance between them is shrinking is also the sum of their individual rates.
Examples
Dale left
his high school at 3:45 and walked towards his brother’s school at 5 mph. His
brother, Jason, left his elementary school at the same time and walked toward
Dale’s high school at 3 mph. If their schools are 2 miles apart, when will they
meet?
The rate at which the brothers are moving
towards each other is
3 + 5 = 8
mph. Let t represent the number of hours the boys walk.
The boys
will meet after ¼ an hour or 15 minutes; that is, at 4:00.
A jet
airliner leaves Dallas going to Houston, flying at 400 mph. At the same time,
another jet airliner leaves Houston, flying to Dallas, at the same rate. How
long will it take for the two airliners to meet? (Dallas and Houston are 250
miles apart.) The distance between the jets is decreasing at the rate of 400 +
400 = 800 mph. Let t represent the number of hours they are flying.
The planes
will meet after 5/16 hours or 60 (5/16) = 18 ¾ minutes or 18 minutes 45 seconds.
Practice
1. Jessie
leaves her house on a bicycle, traveling at 8 mph. She is going to her friend
Kerrie’s house. Coincidentally, Kerrie leaves her house at the same time and
rides her bicycle at 7 mph to Jessie’s house. If they live 5 miles apart, how
long will it take for the girls to meet?
2. Two
cars 270 miles apart enter an interstate highway traveling towards one another.
One car travels at 65 mph and the other at 55 mph. When will they meet?
3. At
one end of town, a jogger jogs southward at the rate of 6 mph. At the opposite
end of town, at the same time, another jogger heads northward at the rate of 9
mph. If the joggers are 9 miles apart, how long will it take for them to meet?
Solutions
1. The
distance between the girls is decreasing at the rate of 8 + 7 = 15 mph. Let t
represent the number of hours they are on their bicycles.
The girls will meet in ⅓ of an hour or 20 minutes.
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.
The cars will meet after 2 ¼ 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.
The
joggers will meet after ⅗ of an hour or 60(⅗) = 36 minutes.
“Sumber Informasi”
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