SOLUTION: Suppose that a cyclist began a 352 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

Algebra ->  Expressions-with-variables -> SOLUTION: Suppose that a cyclist began a 352 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      Log On


   

Question 1108025: Suppose that a cyclist began a 352

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 5.5

hr and the car traveled 32.8

mph faster than the​ bicycle, find the average rate of each
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that a cyclist began a 352 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 5.5 hr and the car traveled 32.8 mph faster than the​ bicycle,
find the average rate of each
:
let s = the speed of the bike
then
(s+32.8) = the speed of the car
:
Both travel for 5.5 hrs and the sum of their distances is 352 mi
(dist = time * speed)
5.5s + 5.5(s+32.8) = 352
5.5s + 5.5s + 180.4 = 352
11s = 352 - 180.4
11s = 171.6
s = 171.6/11
s = 15.6 mph is the speed of the bike
then, obviously
15.6 + 32.8 = 48.4 mph is the speed of the car
:
;
Confirm this, find the distance each traveled
5.5*15.6 = 85.8 mi
5.5*48.4 = 266.2 mi
--------------------
total dist: 352.0