Question 833439: In a bicycle race over a 20 km route, Danny finished 8 minutes ahead of John. Danny pedaled 5 km per hour faster than John. What was Danny's rate
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625)   (Show Source):
You can put this solution on YOUR website! Uniform rates for travel, using  .
This example is in kilometers and hours.
8 minutes is  hour
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Let t = time for John to finish the race
______________speed_____________time_______________distance(km)
Danny_________(___)_____________t-8/60_____________20
John_________(____)______________t_________________20
Danny is at a rate r+5, if John went at a rate of r. The rates are unknown.
This and also reducing the time expression for Danny,...
______________speed_____________time_______________distance(km)
Danny_________(r+5)_____________t-2/15_____________20
John_________(r)_________________t_________________20
A rate*time=distance equation can be made for each of Danny and John.
John:  , which can also be used as 
Danny: 
Substituting with John's equation,
Multiply members by 15 to clear the denominators
Make use of John's equation:
 ----Quadratic equation in r, the rate for John.
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Use the * general solution to a quadratic equation to solve for r, even through the question really just asks for Danny's rate; both rates are given a relationship in the description.
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* The quadratic expression on the left hand side is factorable, so you might be able to explore the factorizations of 750, but you will find that the equation is  .
The meaningful answer is,  . This means, Danny's rate was 35 kilometers per hour.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website!
In a bicycle race over a 20 km route, Danny finished 8 minutes ahead of John. Danny pedaled 5 km per hour faster than John. What was Danny's rate
Danny's speed:  km/h
You can do the check!!
If you need a complete and detailed solution, let me know!!
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