SOLUTION: On a recent trip, Sarahs car traveled 20 mph faster on the first 200 miles that it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarahs

Question 336203: On a recent trip, Sarahs car traveled 20 mph faster on the first 200 miles that it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarahs car on the first part of the trip.
a) 13 mph b) 77 mph c) 68 mph d) 57 mph
I came up with b) 77 but was not sure if this was correct. Could you please show me the correct way to work this problem out.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
On a recent trip, Sarahs car traveled 20 mph faster on the first 200 miles that
it did on the remaining 80 miles.
The total time for the trip was 4 hours. Find the speed of Sarahs car on the first part of the trip.
:
Let s = speed on the 1st part of the trip (200 mi)
then
(s-20) = speed on the last part (80 mi)
:
Write a time equation: time = dist/speed
:
Fast speed time + slow speed time = 4 hrs
+ = 4
multiply equation by s(s-20),results:
200(s-20) + 80s = 4s(s-20)
:
200s - 4000 + 80s = 4s^2 - 80s
:
280s - 4000 = 4s^2 - 80s
A quadratic equation
0 = 4s^2 - 80s - 280s + 4000
:
4s^2 - 360s + 4000 = 0
simplify divide by 4
s^2 - 90s + 1000 = 0
Solving this with quadratic formula got two solutions: s=13 and s=77
Obviously s = 77 mph is the one
:
:
Check it find the time at each speed
200/77 = 2.6 hr
80/57 = 1.4 hrs
-----------------
total time 4 hrs
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