SOLUTION: Two cyclist start from the same point and ride in opposite directions. One cyclist rides 5 mph faster than the other. In 5 hour the cyclists are 175 mile apart. Find the rate of th

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Question 176342: Two cyclist start from the same point and ride in opposite directions. One cyclist rides 5 mph faster than the other. In 5 hour the cyclists are 175 mile apart. Find the rate of the slower cyclist.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Distance(d) equals rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate of slower cyclist
Then r+5=rate of faster cyclist
Distance slower cyclist travels in 5 hours=5r
Distance faster cyclist travels in 5 hours=5(r+5)
Now we are told in a roundabout way that the sum of the above distances equals 175 mi, so:
5r+5(r+5)=175 get rid of parens
5r+5r+25=175 subtract 25 from each side
10r+25-25=175-25 collect like terms
10r=150 divide each side by 10
r=15 mph------------------------------------rate of slower cyclist
r+5=15+5=20 mph----------------------------rate of faster cyclist
CK
5*15+5*20=175
75+100=175
175=175
Does this help??-----ptaylor