SOLUTION: My friend and I live 120 miles apart. We decided to ride our bikes to meet one another between our homes. We both started out at 7 am and I thought it would take all day to meet. T

Question 939216: My friend and I live 120 miles apart. We decided to ride our bikes to meet one another between our homes. We both started out at 7 am and I thought it would take all day to meet. To my surprise, 2 hours later there was my friend in the road! It turns out that he took his motorcycle instead of a bicycle. If my friend traveled 4 times faster than I was riding my bike, how fast was i bicycling?
Found 2 solutions by TimothyLamb, Alan3354:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = speed of bike (mph)
y = speed of motorcycle (mph)
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speed of bike and motorcycle relative to each other:
s = x + y
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y = 4x
---
s = d/t
s = 120/2
s = 60
---
equate s's:
x + y = 60
---
linear system:
y = 4x
x + y = 60
---
put the system of linear equations into standard form
---
4x - y = 0
x + y = 60
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = 12
y = 48
---
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Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
My friend and I live 120 miles apart. We decided to ride our bikes to meet one another between our homes. We both started out at 7 am and I thought it would take all day to meet. To my surprise, 2 hours later there was my friend in the road! It turns out that he took his motorcycle instead of a bicycle. If my friend traveled 4 times faster than I was riding my bike, how fast was i bicycling?
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You travel the same amount of time until you meet.
--> the distances each travels is directly related to the speeds.
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4x faster = 5x as fast.
The motorcycle goes 5x as far as the bicycle.
--> 100 miles and 20 miles
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PS if 4x faster = 4x as fast, what is 1x faster, or 100% faster? Is it the same speed?
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