SOLUTION: the word problem i am having trouble completing has different distances, and that is where i get confused. Thank you so much, in advance A cyclist travels 20 miles in the same a

Question 112722: the word problem i am having trouble completing has different distances, and that is where i get confused. Thank you so much, in advance
A cyclist travels 20 miles in the same amount of time as it takes a hiker to walk 6 miles. The rate of the cyclist is 7 mph faster than the rate of the hiker. Find the rate of the cyclist and the rate of the hiker.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
---EVEN THOUGH THE DISTANCES ARE DIFFERENT, THE TIMES ARE THE SAME AND THAT GIVES US THE BASIS FOR SETTING UP AN EQUATION.
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate of the hiker
Then r+7=rate of the cyclist
time for the hiker=6/r
time for the cyclist=20/(r+7)
And we are told that the above two times are the same. So:
6/r=20/(r+7) multiply each term by r(r+7)
6(r+7)=20r get rid of parens
6r+42=20r subtract 6r from both sides
6r-6r+42=20r-6r collect like terms
14r=42 divide both sides by 14
r=3 mph-------------------------rate of the hiker
r+7=3+7=10 mph------------------rate of the cyclist
CK
time for hiker=6/3=2 hrs
time for cyclist=20/10=2 hrs

Hope this helps---ptaylor

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