SOLUTION: Kathy bikes 7km/h faster than Dan. In the same time it takes Dan to bike 45 km, Kathy can bike 66 km. How fast does each person travel?

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Question 1108489: Kathy bikes 7km/h faster than Dan. In the same time it takes Dan to bike 45 km, Kathy can bike 66 km. How fast does each person travel?
Found 3 solutions by josgarithmetic, stanbon, ikleyn:
Answer by josgarithmetic(39614)   (Show Source): You can put this solution on YOUR website!
              SPEED        TIME         DISTANCE
Kathy         r+7            t           66
Dan            r             t           45

Their times are equal.



-----solve this for r.




.
.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Kathy bikes 7km/h faster than Dan. In the same time it takes Dan to bike 45 km, Kathy can bike 66 km. How fast does each person travel?t hr
------
Dan DATA:
dist = 45 km ; time = t hrs ; rate = 45/t km/hr
--------------------
Kathy DATA:
dist = 66 km ; time = t hrs ; rate = 66/t km/hr
--------------------
Equation:
Kathy rate = Dan rate + 7 km/hr
-----
66/t -45/t = 7
-----
66-45 = 7t
21 = 7t
time = 3 hrs
------
Kathy rate = 66/3 = 22 km/hr
Dan rate = 45/3 = 15 km/hr
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Cheers,
Stan H.
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Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.
The "time" equation is

 =       ("it takes "the same time" . . . )


===========>  45*(r+7) = 66r,


45*7 + 45r = 66r,

45*7 = 66r - 45r = 21r  ====>  r =  = 15.


Answer.  Dan's rate is 15 km/h.  Kathy rate is 15+7 = 22 km/h


Check.   = 3 = .   ! Correct !


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