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(39613)   (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
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Dan DATA:
dist = 45 km ; time = t hrs ; rate = 45/t km/hr
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Kathy DATA:
dist = 66 km ; time = t hrs ; rate = 66/t km/hr
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Equation:
Kathy rate = Dan rate + 7 km/hr
-----
66/t -45/t = 7
-----
66-45 = 7t
21 = 7t
time = 3 hrs
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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(52754)   (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 !