SOLUTION: -Applications of Quadratic Equations during a bicycle race, suppose that on one particular day, the racers must complete 210 mi. One Cyclist, traveling 10 mph faster than the seco

Question 419407: -Applications of Quadratic Equations
during a bicycle race, suppose that on one particular day, the racers must complete 210 mi. One Cyclist, traveling 10 mph faster than the second cyclist, covers this distance in 2.4 h less time than the second cyclist. Find the rate of the first cyclist.
I am so confused on how to do word problems dealing with quadratic equations...
please email me asap!
Thank you so much
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Always remember that with d = r*t problems, each thing that is
moving must have it's own equation, and each equation must
refer to 1 and only 1 person or thing that is moving.
Both cyclists go the same distance: mi
Let = time for 2nd cyclist
Let = speed for the 2nd cyclist
-----------------------
1st cyclist:
(1)
2nd cyclist:
(2)
----------------
Note that there are 2 equations and 2 unknowns,
so this is solvable.
(1)
(1)
and, from (2)
(2)
-----------------
Substituting from (2) into (1):
(1)
(1)
Multiply both sides by
(1)
(1)
Divide through by
(1)
Use the quadratic equation

(note: the negative root gives a negative answer-can't use it)

The 1st cyclist's rate is

The 1st cyclist's speed is 35 mi/hr
check answer:
(1)
(1)
(1)
(1)
(1)
-------------
(2)
(2)
(2)
OK
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