SOLUTION: Two cyclists, 25 KM apart set out at the same time and meet in 50 minutes. Had they been cycling in the same direction the faster would have overtaken the slower in 5 hours. Find t
Question 1058008: Two cyclists, 25 KM apart set out at the same time and meet in 50 minutes. Had they been cycling in the same direction the faster would have overtaken the slower in 5 hours. Find their cycling speeds. Found 2 solutions by josmiceli, ikleyn:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! In both these cases, you can think of
it as one of the cyclists moving and the
other one standing still.
-----------------------------
When they are moving towards eachother,
the moving one moves at the sum of their speeds
---------------------------------------------
When moving in the same direction, let =
the distance the slower one travels until the
faster one catches up.
Moving towards eachother:
(1)
Moving in the same direction:
Slower one:
(2)
Faster one:
(3)
-------------------------
(1)
(1)
--------------------------
(2)
(3)
--------------------------
plug (2) and (3) into (1)
(1)
(1)
(1)
(1)
--------------------------------
(2)
(2)
(2)
--------------------------
(3)
(3)
(3)
(3)
-----------------------------
The faster one's speed is 17.5 km/hr
The slower one's speed is 12.5 km/hr
-----------------------------------
check answer:
(1)
(1)
(1)
----------------------
(2)
(2)
(2) km
-----------------------
(3)
(3)
(3)
(3) km
-----------------------
OK
You can put this solution on YOUR website! .
Two cyclists, 25 KM apart set out at the same time and meet in 50 minutes. Had they been cycling in the same direction
the faster would have overtaken the slower in 5 hours. Find their cycling speeds.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Moving toward each other:
= 25, which is the same as
= , or
= 30 . (1)
Moving in one direction:
= , which is the same as
25 = , or
= = 5 . (2)
where is the faster' speed and is the slower' speed, in .
Rewrite (1) and (2) as the system:
= 30, (1')
= 5. (2')
Add the two equations (1') and (2'). You will get
= 35 ---> = 17.5 .
Then = 30 - 17.5 = 12.5 Answer. Faster 17.5 ; slower 12.5 .
