SOLUTION: A student plans to drive at night from Albuquerque to Dallas. He will drive 253 miles in New Mexico at 75 mph, then 410 miles in Texas at 65 mph. The equation for this is T(a)

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Question 457835: A student plans to drive at night from Albuquerque to Dallas. He will drive 253 miles in New Mexico at 75 mph, then 410 miles in Texas at 65 mph.
The equation for this is T(a) = 253/a+75 + 410/a+65
By how much would he have to exceed the speed limits for the driving time to be 9 hours?..
Then it says to verify by using a graphing calc.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A student plans to drive at night from Albuquerque to Dallas.
He will drive 253 miles in New Mexico at 75 mph, then 410 miles in Texas at 65 mph.
The equation for this is T(a) = 253/a+75 + 410/a+65
By how much would he have to exceed the speed limits for the driving time to be 9 hours?.
a = amt he exceeds the speed limit
:
253%2F%28%28a%2B75%29%29 + 410%2F%28%28a%2B65%29%29 = 9 hrs
:
multiply by (a+75)(s+65), results
253(a+65) + 410(a+75) = 9(a+65)(a+75)
:
253a + 16445 + 410a + 30750 = 9(a^2 + 140a + 4875)
:
663a + 47195 = 9a^2 + 1260a + 43875
Combine on the right
0 = 9a^2 + 1260a - 663a + 43875 - 47195
:
9a^2 + 597a - 3320 = 0
Solve this equation using the quadratic formula; a=9, b=597, c=-3320
you should get a positive solution:
a = 5.16 mph above the speed limits, to complete the trip in 9 hrs
:
:
Then it says to verify by using a graphing calc.
you can graph y = 253%2F%28%28x%2B75%29%29 + 410%2F%28%28x%2B65%29%29, where
x = amt above the speed limit
y = time in hrs to complete the trip

you can see when x=5, y=9 (green line)