SOLUTION: I have been trying for two hours to get this, but I can't. Can someone PLEASE help??? A car and a bike set out at noon from the same point headed in the same direction. At 1:00

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: I have been trying for two hours to get this, but I can't. Can someone PLEASE help??? A car and a bike set out at noon from the same point headed in the same direction. At 1:00      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 120632This question is from textbook Algebra Structure and Method
: I have been trying for two hours to get this, but I can't. Can someone PLEASE help???
A car and a bike set out at noon from the same point headed in the same direction. At 1:00 P.M., the car is 60 km ahead of the bike. Find how fast each travels, given that the car travels four times as fast as the bike. This question is from textbook Algebra Structure and Method

Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A car and a bike set out at noon from the same point headed in the same direction. At 1:00 P.M., the car is 60 km ahead of the bike. Find how fast each travels, given that the car travels four times as fast as the bike.
:
Let s = speed of the bike
then
4s = speed of the car
:
The travel time for both is given as 1 hr (noon to 1PM):
:
write a distance equation Distance = time * speed
:
Car dist - bike dist = 60 km
1(4s) - 1s = 60
4s - s = 60
3s = 60
s = 60%2F3
s = 20 km/hr is the speed of the bike
then
4*20 = 80 km/hr is the speed of the car
:
:
Confirm solutions by finding distance traveled by each:
1*80 = 80 km
1*20 = 20 km
-------------
dif = 60 km as given

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I need to use d+=+r%2At. There is a separate equation for
bike and car
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
Call the distance the car travels d%5Bb%5D+%2B+60 km
Then the distance the bike travels is d%5Bb%5D km
Given: r%5Bc%5D+=+4%2Ar%5Bb%5D
We are starting a stopwatch at noon and stopping it at 1:00 PM, so
t%5Bb%5D+=+1 hr
t%5Bc%5D+=+1 hr
d%5Bb%5D+=+r%5Bb%5D%2A1
d%5Bb%5D+%2B+60+=+4%2Ar%5Bb%5D%2A1
substitute r%5Bb%5D%2A1 for d%5Bb%5D in the 2nd equation
r%5Bb%5D+%2B+60+=+4%2Ar%5Bb%5D
3%2Ar%5Bb%5D+=+60
r%5Bb%5D+=+20 km/hr answer
r%5Bc%5D+=+4%2A20
r%5Bc%5D+=+80 km/hr answer
check
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
----------------------
d%5Bb%5D+=+20%2A1
d%5Bc%5D+=+80%2A1
The difference is 60 km
OK