SOLUTION: Thelma's average driving speed is 3 miles per hour faster than Doug's. In the same length of time it takes Thelma to drive 200 miles, Doug only drives 188 miles. What is Thelma's

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Thelma's average driving speed is 3 miles per hour faster than Doug's. In the same length of time it takes Thelma to drive 200 miles, Doug only drives 188 miles. What is Thelma's      Log On

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Question 197729: Thelma's average driving speed is 3 miles per hour faster than Doug's. In the same length of time it takes Thelma to drive 200 miles, Doug only drives 188 miles. What is Thelma's average driving speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I have an equation for each one
d%5Bt%5D+=+r%5Bt%5D%2At%5Bt%5D
and
d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D
---------------------
given:
r%5Bt%5D+=+r%5Bd%5D+%2B+3 mi/hr
t%5Bt%5D+=+t%5Bd%5D (I'll call them both t)
d%5Bt%5D+=+200 mi
d%5Bd%5D+=+188 mi
---------------------
What is Thelma's average driving speed?
d%5Bt%5D+=+r%5Bt%5D%2At%5Bt%5D
200+=+r%5Bt%5D%2At
200+=+%28r%5Bd%5D+%2B+3%29%2At
and
d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D
188+=+r%5Bd%5D%2At
r%5Bd%5D+=+188%2Ft
Substituting,
200+=+%28188%2Ft+%2B+3%29%2At
200+=+188+%2B+3t
3t+=+12
t+=+4 hr
Substituting,
200+=+r%5Bt%5D%2At
r%5Bt%5D+=+200%2F4
r%5Bt%5D+=+50
Thelma's average driving speed was 50 mi/hr
check:
r%5Bt%5D+=+r%5Bd%5D+%2B+3 mi/hr
50+=+r%5Bd%5D+%2B+3
r%5Bd%5D+=+47 mi/hr
d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D
188+=+47%2A4
188+=+188
and
d%5Bt%5D+=+r%5Bt%5D%2At%5Bt%5D
200+=+50%2A4
200+=+200
OK