SOLUTION: Two cyclist ride in opposite directions and after 3 hours they are 87 kilometres from each other.if however they ride in the same direction the one is 9 km ahead of the other,after

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Question 771600: Two cyclist ride in opposite directions and after 3 hours they are 87 kilometres from each other.if however they ride in the same direction the one is 9 km ahead of the other,after 3 hours.determine each one's velocity.

Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Two cyclist ride in opposite directions and after 3 hours they are 87 kilometres from each other.if however they ride in the same direction the one is 9 km ahead of the other,after 3 hours.determine each one's velocity.
let speed of one be x and the other y kph
Case I
they are moving away. add their speeds
d=rt
(x+y)*3=87
/3
x+y=29....................(1)
distance traveled by first is 3x
distance traveled by second = 3Y
3X-3Y=9
/3
X-Y=3.............................(2)
add (1) & (2)
2x=32
/2
x=16 speed of first is 16 kph
x-y=3
plug x=16
speed of second = 13 kph

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Their velocities add when they are going
in opposite directions, and their velocities
subtract when they are going in the same direction
------------------
In the 1st case, think of one cyclist as standing still
and the other one traveling at the sum of their speeds
In the 2nd case, think of one cyclist as standing still
and the other one traveling at the difference of their speeds
------------------
Let = the speed of the slower cyclist
Let = the speed of the faster cyclist
(1)
(2)
-------------------------
(1)
(2)
Add the equations

and, since
(2)
(2)
(2)
Their speeds are 16 km/hr and
13 km/hr
---------
check:
(1)
(1)
(1)
(1)
OK