SOLUTION: Sally was able to drive an average of 29 miles per hour faster in her car after the traffic cleared. She drove 29 miles in traffic before it cleared and then drove another 174 mile

Question 1090368: Sally was able to drive an average of 29 miles per hour faster in her car after the traffic cleared. She drove 29 miles in traffic before it cleared and then drove another 174 miles. If the total trip took 4 hours, then what was her average speed in traffic?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Sally was able to drive an average of 29 miles per hour faster in her car after the traffic cleared.
She drove 29 miles in traffic before it cleared and then drove another 174 miles.
If the total trip took 4 hours, then what was her average speed in traffic?
:
let s = the speed in traffic
then
(s+29) = normal speed
:
Write a time equation; time = dist/speed
Traffic time + highway time = 4 hrs
+ = 4
multiply eq by s(s+29)
s(s+29)* + s(s+29) = 4s(s+29)
cancel denominators
29(s+29) + 174s = 4s^2 + 116s
29s + 841 + 174s = 4s^2 + 116s
203s + 841 = 4s^2 + 116s
Arrange as a quadratic equation
0 = 4s^2 + 116s - 203s - 841
4s^2 - 87s - 841 = 0
Use the quadratic formula to find s; a=4; b=-87; c=-841
I got a positive solution
s = 29 mph in traffic
:
:
Check this, find the actual time at each speed
174/58 = 3 hrs
29/29 = 1 hr
--------------
total time = 4 hrs

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