Question 1060146
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"What was the cyclists speed?" is the ultimate question here. Since it's unknown and we want to find it, let's make


x = cyclists speed in miles per hour.


The runner is 14 mph slower than the cyclist, so the runner's speed is x-14 miles per hour.


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We will use the formula


distance = rate*time


"rate" is another term for "speed". In short, 


d = r*t


The distance for the runner is 3 miles. So d = 3 for the runner. The value of t is unknown. Let's just leave it as t for now.


So 
d = r*t
turns into
3 = (x-14)*t
after replacing the variables with the expressions set up earlier. 


Similarly, for the cyclist, this equation
d = r*t
turns into
10 = x*t



We can solve for t in that other equation to get


10 = x*t
10/x = t
t = 10/x


Then let's plug that into the first equation


3 = (x-14)*t
3 = (x-14)*(10/x) ... replace t with 10/x


Now isolate x


3 = (x-14)*(10/x)
3*x = (x-14)*(10/x)*x ... multiply both sides by x
3x = 10(x-14)
3x = 10x - 140
3x - 10x = -140
-7x = -140
x = 20 ... divide both sides by -7


So that's why the cyclist's speed is 20 mph. 


Let me know if this helps or not. Thank you. 
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