SOLUTION: Jim drives from the Twin Cities to Monroe Louisiana, a distance of 1075 miles in record time. On the way back he averages 5 mph slower and the trip takes an additional 1.5 hrs. H

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Jim drives from the Twin Cities to Monroe Louisiana, a distance of 1075 miles in record time. On the way back he averages 5 mph slower and the trip takes an additional 1.5 hrs. H      Log On


   

Question 192729: Jim drives from the Twin Cities to Monroe Louisiana, a distance of 1075 miles in record time. On the way back he averages 5 mph slower and the trip takes an additional 1.5 hrs. How fast did he drive to Monroe LA.? Round to the nearest tenth of a mph.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Jim drives from the Twin Cities to Monroe Louisiana, a distance of 1075 miles
in record time. On the way back he averages 5 mph slower and the trip takes
an additional 1.5 hrs. How fast did he drive to Monroe LA.?
Round to the nearest tenth of a mph.
:
let s = his original speed to La
then
(s-5) = his return speed
;
Write a time equation: Time = dist%2Fspeed
;
Time to + 1.5 hr = time to return
1075%2Fs + 1.5 = 1075%2F%28%28s-5%29%29
Multiply equation by s(s-5), results
1075(s-5) + 1.5s(s-5) = 1075s
:
1075s - 5375 + 1.5s^2 - 7.5s - 1075s = 0
:
1.5s^2 - 7.5s - 5375 = 0
:
A quadratic equation, use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: x = s; a = 1.5, b = -7.5, c = -5375
s+=+%28-%28-7.5%29+%2B-+sqrt%28-7.5%5E2+-+4+%2A+1.5+%2A+-5375+%29%29%2F%282%2A1.5%29+
:
s+=+%287.5+%2B-+sqrt%2856.25+-+%28-32250%29+%29%29%2F%283%29+
:
s+=+%287.5+%2B-+sqrt%2856.25+%2B+32250+%29%29%2F%283%29+
:
s+=+%287.5+%2B-+sqrt%2832306.25+%29%29%2F%283%29+
Two solutions but we only want the positive one:
s+=+%287.5+%2B+179.74%29%2F%283%29+
s+=+187.24%2F3+
s = 62.4 mph to Monroe La
:
:
Check solution by finding the time for each trip; return speed: 62.4 - 5 = 57.4
1075/57.4 = 18.73 hrs
1075/62.4 = 17.23 hrs
-----------------------
difference: 1.5 hrs