SOLUTION: On a recent trip, Sarah's car traveled 20 mph faster on the first 100 miles than it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarah'

Question 25807: On a recent trip, Sarah's car traveled 20 mph faster on the first 100 miles than it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarah's car on the first part of the trip
Answer by atif.muhammad(135) (Show Source): You can put this solution on YOUR website!
Let's divide the journey into 2 parts:
1.
Let x equal the speed of Sarah's car for the first part.
The distance is 100 miles
Time take to travel : (100/x) hrs

2.
Let (x-20) equal speed of Sarah's car for the second part.
As Sarah was driving 20 miles slower in the second part than the first part and her speed for the first part was, x, her speed for the second part must be (x-20) mph.
The distance is 80 miles
Time taken to travel: [80/(x-20)] hrs

--------
The total time taken is 4 hrs.
Therefore:
(100/x) + [80/(x-20)] = 4
(100x - 2000 + 80x)/[x(x-20)] = 4
180x-2000 = 4x(x-20)
180x - 2000 = 4x^2 - 80x
0 = 4x^2 - 260x + 2000
2x^2 - 130x + 1000 = 0
x^2 - 65x + 500 = 0
x = 56,9
The speed of Sarah's car for the first part of the trip is either 56 or 9 mph.
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