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

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?
:
Let c = speed that John can cycle
Let d = speed Steve can drive
:
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)
:
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
:
Replace s with (c+25)
- = 1.5
:
Multiply by c(c+25), results
75(c+25) - 75c = 1.5c(c+25)
75c + 1875 - 75c = 1.5c^2 + 37.5c
:
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
:
You can solve this using the quadratic formula, but this will factor to
(3c + 150)(c - 25) = 0
:
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
---------------
differ: 1.5 hrs

RELATED QUESTIONS
In one hour, Ed drives 25 miles farther in his car than Frank can cycle on his bike. If... (answered by josmiceli)

george can ride his bike to work in 3/4 hour. if he takes his car to work, the trip takes (answered by lwsshak3,josmiceli)

Johnny gets to work in 1/2 hour when he drives his car. Riding his bike (by the same... (answered by ankor@dixie-net.com)

jason rides his bike 6 miles in the same time it takes steve to ride 8 miles. if jason... (answered by ewatrrr)

if a man walks for 20 minutes and then drives in his car for an hour and a half he goes a (answered by checkley79,josmiceli)

Paul leaves his house on a bike riding at 15 mph, one hour later, Ray leaves in his car... (answered by Paul)

It takes Brian 15 hours longer to model a car than it takes John. If they work together,... (answered by josgarithmetic,MathTherapy)

John can travel 56 mi on his motorcycle in the same time it takes roger to travel 21 mi... (answered by richwmiller)

harry drives his car for 15 miles at a certain speed. he then increases his speed by 10... (answered by josgarithmetic)