SOLUTION: on a monday afternoon practice, two cyclists took the same amount of time to ride 39 miles and 30 miles, respectively. if a cyclist rode 3 mph faster than the other, what is the ra

Question 1043847: on a monday afternoon practice, two cyclists took the same amount of time to ride 39 miles and 30 miles, respectively. if a cyclist rode 3 mph faster than the other, what is the rate of each rider?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
on a monday afternoon practice, two cyclists took the same amount of time to ride 39 miles and 30 miles, respectively. if a cyclist rode 3 mph faster than the other, what is the rate of each rider?
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Assuming the faster rider went the further distance,
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Faster rider DATA:
rate = x+3 mph ; distance = 39 miles ; time = d/r = 39/(x+3) hrs
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Slower rider DATA:
rate = x mph ; distance = 30 miles ; time = d/r = 30/x hrs
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Equation:
time = time
30/x = 39/(x+3)
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30x + 90 = 39x
9x = 90
x = 10 mph (slower rider rate)
x+3 = 13 mph (faster rider rate)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The faster rider rode 39 mi in the same time
Let = the speed of the slower rider in mi/hr
= the speed of the faster rider in mi/hr
Let = time in hrs for both riders
-----------------------------------------
Equation for slower rider:
(1)
Equation for faster rider:
(2)
-----------------------
(1)
Substitute (1) into (2)
(2)
(2)
(2)
(2)
(2)
and

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Their speeds were 10 mi/hr and 13 mi/hr
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check:
(1)
(1) hrs
and
(2)
(2)
(2) hrs
OK
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