SOLUTION: One morning Madeline drove 5 hours before stopping to eat. After lunch, she increased her speed by 10mph in order to complete a 430-mile trip in 8 hours of driving time. How fast d

Question 508036: One morning Madeline drove 5 hours before stopping to eat. After lunch, she increased her speed by 10mph in order to complete a 430-mile trip in 8 hours of driving time. How fast did Madeline drive in the morning?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One morning Madeline drove 5 hours before stopping to eat. After lunch, she increased her speed by 10mph in order to complete a 430-mile trip in 8 hours of driving time. How fast did Madeline drive in the morning?
-----------------------
Morning DATA:
time = 5 hrs ; rate = r mph ; distance = 5r miles
-----
Afternoon DATA:
rate = r+10 mph ; time = 8-5 = 3 hrs ; distance = 3(r+19) miles
----------------
Equation:
distance + distance = 430 miles
5r + 3r+ 57 = 430
8r = 373
r = 46.63 mph (morning rate)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = her speed before lunch
= her speed after lunch
hrs driving time after lunch
Let = distance she drove before lunch
= distance she drove after lunch
-------------
Before lunch:
(1)
After lunch:
(2)
Substitute (1) into (2)
(2)
(2)
(2)
(2)
She drove 50 mi/hr in the morning
check:

(1)
(1)
and
(2)
(2)
OK
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