SOLUTION: Two cyclists travel 210 miles. One cyclist, traveling 10 mph faster than the second cyclist, covers the distance in 2.4 hours less than the second cyclist. Find the rate of the fi

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Question 1078376: Two cyclists travel 210 miles. One cyclist, traveling 10 mph faster than the second cyclist, covers the distance in 2.4 hours less than the second cyclist. Find the rate of the first cyclist.
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52848) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "r" be the rate of the first cyclist, in mph.

Then the rate of the second cyclist is (r-10) mph.

The condition says:

210%2F%28r-10%29+-+210%2Fr = 2.4.


It is your "time equation" to solve for r.


To solve it, multiply oth sides by r*(r-10). You will get

210r - 210(r-10) = 2.4r*(r-10).


Simplify and solve this quadratic equation for "r". It is just arithmetic.


Good luck !

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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two cyclists travel 210 miles.
One cyclist, traveling 10 mph faster than the second cyclist, covers the distance in 2.4 hours less than the second cyclist.
Find the rate of the first cyclist.
:
let s = the speed of the 1st cyclist
then
(s-10) = the speed of the 2nd cyclist
:
Write a time equation; time = dist/speed
2nd cyclist time - 1st cyclist time = 2.4 hrs
210%2F%28%28s-10%29%29 - 210%2Fs = 2.4
multiply equation by s(s-10)
s(s-10)*210%2F%28%28s-10%29%29 - s(s-10)*210%2Fs = 2.4s(s-10)
cancel denominators
210s - 210(s-10) = 2.4s^2 - 24s
210s - 210s + 2100 = 2.4s^2 - 24s
arrange as a quadratic equation
2.4s^2 - 24s - 2100 = 0
simplify, divide by 2.4
s^2 - 10s - 875 = 0
You can use the quadratic formula; a=1; b=-10; c=-875, but this will factor
(s+25)(s-35) = 0
The positive solution
s = 35 mph is speed of the 1st cyclist
:
:
:
Check this by finding the actual time of each cycle
210/25 = 8.4 hrs the time of the 2nd cyclist
210/35 = 6.0 hrs for the 1st cyclist
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time dif:2.4 hrs