Question 173625This question is from textbook Introductory Algebra
: Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 84 miles in the same time that Dana travels 78 miles. If Chuck's rate of travel is 3 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?
This question is from textbook Introductory Algebra
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let t = amount of time they traveled.
let r1 = rate of travel of chuck
let r2 = rate of trave of dana
chuck travels 84 miles.
dana travels 78 miles.
chuck's rate of speed is 3 mph more than dana's.
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r*t = d
for chuck:
r1*t = 84
for dana:
r2*t = 78
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solving for t, the equations becomes:
t = 84/r1
t = 78/r2
since both equations equal t, they are equal to each other, so:
84/r1 = 78/r2
if we cross multiply, we get:
78*r1 = 84*r2
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since chuck travels 3 mph faster than dana, then:
r1 = r2+3
substituting, we get:
78*(r2+3) = 84*(r2)
multiplying out, we get:
78*r2 + 234 = 84*r2
subtracting 78*r2 from both sides of equation, we get:
234 = 84*r2-78*r2
simplifying, we get:
234 = 6*r2
dividing both sides of equation by 6, we get:
234/6 = r2
simplifying, we get:
r2 = 39 mph.
this makes r1 = 39 + 3 = 42 mph.
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chuck travels 42 mph
dana travels 39 mph.
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chuck's equation becomes:
r*t = d
42*t = 84
t = 2 hours
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dana's equation becomes:
r*t = d
39*2 = 78
78 = 78
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this checks out.
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answer to the question is:
chuck travels at 42 mph.
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