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?
:
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
{{{75/c}}} - {{{75/d}}} = 1.5
:
Replace s with (c+25)
{{{75/c}}} - {{{75/((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
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differ: 1.5 hrs