SOLUTION: Roman and Jems traveled to a nearby playground with their bikes. They decided to ride back and forth across the playground. Both of them ride at a constant speed (although their sp
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Question 867518: Roman and Jems traveled to a nearby playground with their bikes. They decided to ride back and forth across the playground. Both of them ride at a constant speed (although their speeds do not equal each other) and they each take no time to turn around at each end of the playground. Roman starts at the west end and Jems starts at the east end. They start at the same time and ride towards each other. They meet and pass each other 30 feet from the east end. When they reach the opposite end of the playground, they turn around and ride back towards each other. They meet again 14 feet from the west end of the playground. What is the length of the playground? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Both of them ride at a constant speed (although their speeds do not equal each other) and they each take no time to turn around at each end of the playground.
Roman starts at the west end and Jems starts at the east end.
They start at the same time and ride towards each other.
They meet and pass each other 30 feet from the east end.
When they reach the opposite end of the playground, they turn around and ride back towards each other.
They meet again 14 feet from the west end of the playground.
What is the length of the playground?
|------------------------------d-----------------------------------|
R---------------(d-30)------------------->*<---------30----------J; 1st meeting
J>------14------->*<-------------------(d-14)-------------------<-R; 2nd meeting
:
let d = length of the play ground
First meeting
R travels (d-30),
J travels 30 ft
2nd meeting
J travels: (d-30) + 14, simplifies to (d-16)
R travels 30 + (d-14), simplifies to (d+16)
:
The relationship between R and J's distances is the same for each meeting, therefore =
Cross multiply
(d-30)(d-16) = 30(d+16)
FOIL
d^2 -16d - 30d + 480 = 30d + 480
Combine like terms on the left
d^2 - 46s - 30d + 480 - 480 = 0
d^2 - 76d = 0
Factor out d
d(d - 76) = 0
Two solutions
d = 0
and the one we want
d = 76 ft is the length of the play ground
:
:
We can check this, find the relationships between their travel dist for
each meeting, should be the same.
1st meeting:
R traveled, 76 - 30 = 46 feet
J traveled, 30 ft = 23/15
2nd meeting
R traveled 76 + 16 = 92 ft
J traveled 76 - 16 = 60 ft = 23/15 also
