SOLUTION: A person riding a motorcycle leaves 1 hr after a person riding a bicycle. Both travel the same road. If the person riding the bicycle is traveling at 10mpr and the person riding t

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Question 118440: A person riding a motorcycle leaves 1 hr after a person riding a bicycle. Both travel the same road. If the person riding the bicycle is traveling at 10mpr and the person riding the motorcycle is traveling at 30mpr, how long will it take the motorcycle to overtake the bicycle?
The answer I think is 30min but what is the equation to that?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A person riding a motorcycle leaves 1 hr after a person riding a bicycle. Both travel the same road. If the person riding the bicycle is traveling at 10mpr and the person riding the motorcycle is traveling at 30mpr, how long will it take the motorcycle to overtake the bicycle?
:
That's the right answer but here is a step-by-step method to construct an equation.
:
Let t = time required for the motorcycle to overtake the bike
:
Since the bike left an hour earlier:
(t+1) = travel time of the bike
:
We know when the motorcycle overtakes the bike the will have traveled the same distance.
We can make a simple distance equation from this fact: distance = speed * time
:
Motorcycle dist = bike distance
30t = 10(t+1)
:
30t = 10t + 10
30t - 10t = 10
20t = 10
t =
t = half an hour like you said