SOLUTION: In one hour, Steve drives 25 miles farther in his car than John can cycle on his bike. If it takes John an hour and a half hours longer to cycle seventy five miles than it takes St
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Question 444681: In one hour, Steve drives 25 miles farther in his car than John can cycle on his bike. If it takes John an hour and a half hours longer to cycle seventy five miles than it takes Steve in his car, how fast can John cycle? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! In one hour, Steve drives 25 miles farther in his car than John can cycle on his bike.
If it takes John an hour and a half hours longer to cycle seventy five miles than it takes Steve in his car, how fast can John cycle?
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Let c = speed that John can cycle
Let d = speed Steve can drive
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Write a distance equation for the statement:
"In one hour, Steve drives 25 miles farther in his car than John can cycle on his bike. "
Steve's dist - John's dist = 25
1d - 1c = 25
d = (c + 25)
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Write a time equation for the statement, (time = dist/speed):
"If it takes John an hour and a half hours longer to cycle seventy five miles than it takes Steve in his car,"
John's travel time - Steve's travel time = 1.5 hrs - = 1.5
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Replace s with (c+25) - = 1.5
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Multiply by c(c+25), results
75(c+25) - 75c = 1.5c(c+25)
75c + 1875 - 75c = 1.5c^2 + 37.5c
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Arrange as a quadratic equation
1.5c^2 + 37.5c - 1875 = 0
;
Get rid of those decimals, multiply by 2
3c^2 + 75c - 3750 = 0
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You can solve this using the quadratic formula, but this will factor to
(3c + 150)(c - 25) = 0
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The positive solution
c = 25 mph is the cycling speed
:
:
To check this; find the driving speed
d = c+25
d = 50 mph
Find the time of each
75/25 = 3 hrs
75/50 = 1.5
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differ: 1.5 hrs
