At what speed does Chuck travel?

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Question from Jessica, a student:

This is a word problem of Application of Rational Expressions. This is a algebra math.
Can't figure it out. I don't know how to solve the problem to get to the answer. Thank You.

Solve the problem.

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels

224 miles in the same time that Dana travels 204 miles. If Chuck's rate of travel

is 5 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?

The answer is : 56 mph

Hi Jessica,

The basic fact here is that distance is equal to time times rate. The distance and rate are different for Chuck and Dana so I used

d_c = 224 miles, Chuck's distance
d_d= 204 miles, Dana's distance
r_c = Chuck's rate in mph
r_d = Dada's rate in mph
t = time in hours

You are also told that r_c= r_d + 5

Now write both equations,

d_c = t × r_c and
d_d = t × r_d

Substitute the values you know and solve for t.

I hope this helps,
Harley

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