SOLUTION: A person on a bike is going 18 mph. One hour after the person on a bike leaves, a person in a car is going 45 mph. How long will it take for the person in a car to catch up w

Algebra ->  Algebra  -> Finance -> SOLUTION: A person on a bike is going 18 mph. One hour after the person on a bike leaves, a person in a car is going 45 mph. How long will it take for the person in a car to catch up w      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 178081: A person on a bike is going 18 mph.
One hour after the person on a bike leaves, a person in a car is going 45 mph.
How long will it take for the person in a car to catch up with the bicycle?
Answer by josmiceli(6783) About Me  (Show Source):
You can put this solution on YOUR website!
For the bike, d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
For the car, d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
When they meet, d%5Bb%5D+=+d%5Bc%5D, so I'll just call it d
given:
r%5Bb%5D+=+18 mi/hr
r%5Bc%5D+=+45 mi/hr
So far I have
For the bike, d+=+18%2At%5Bb%5D
For the car, d+=+45%2At%5Bc%5D
Since they're both equal to d, I can say
18%2At%5Bb%5D+=+45%2At%5Bc%5D
Suppose I have a stopwatch and I start it when the car leaves
and I know that the bike left 1 hour ago
I can say t%5Bc%5D+=+t%5Bb%5D+-+1
18%2At%5Bb%5D+=+45%2A%28t%5Bb%5D+-+1%29
18%2At%5Bb%5D+=+45t%5Bb%5D+-+45
27t%5Bb%5D+=+45
t%5Bb%5D+=+5%2F3hr , or in minutes
t%5Bb%5D+=+%285%2F3%29%2A60
%285%2F3%29%2A60+=+100 min
That's 1 hr and 40 min
Since the bike had a 1 hr headstart, the car took 40 min
to catch the bike
check answer:
For the bike, d+=+18%2At%5Bb%5D
For the car, d+=+45%2At%5Bc%5D
d+=+18%2A%285%2F3%29
d+=+30
d+=+45%2A%282%2F3%29
d+=+15%2A2
d+=+30
The distance should be the same for both and it is