SOLUTION: Suppose that a cyclist began a 578 mi ride across a state at the western edge of the&#8203; state, at the same time that a car traveling toward it leaves the eastern end of the sta

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Question 1129892: Suppose that a cyclist began a 578 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after 8.5 hr and the car traveled 37.8 mph faster than the bicycle, find the average rate of each.
Found 2 solutions by josmiceli, addingup:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
You can think of this as one of them
traveling at the sum of their speeds for
the entire distance while the other one
is standing still
Let = the speed of the bike
in mi/hr
= the speed of the car
in mi/hr
-----------------------------------------------

and

-------------------------
The bike's speed was 15.1 mi/hr
The car's speed was 52.9 mi/hr
--------------------------------------
check:

and

and

OK

Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website!
8.5x + 8.5(x + 37.8) = 578
8.5x + 8.5x + 321.38 = 578
17x = 256.7
x = 15.1
.
The bicycle traveled at an average rate of 15.1 mph and the car at an average rate of 52.9 mph (15.1 + 37.8)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:
bike: 8.5 * 15.1 = 128.35
car : 8.5 * 52.9 = 449.65
. . . . . . . . . . -------
. . . . . Total . . :578 Correct

SOLUTION: Suppose that a cyclist began a 578 mi ride across a state at the western edge of the&#8203; state, at the same time that a car traveling toward it leaves the eastern end of the sta

SOLUTION: Suppose that a cyclist began a 578 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the sta