<PRE><B>Question 299899</B>
An express train travels 299 mi. between two cities.
 during the first 111 mi. of a trip, the train traveled through mountainous terrain.
 the train traveled 10 mi. per hour slower through mountainous terrain then through level terrain.
 if the total time to travel between two cities was 7 hours, find the speed of the train on level terrain
:
Let s = train speed thru level terrain
then
(s-10) = speed thru the mountains
:
299 - 111 = 188 mi, dist thru level terrain
:
Write time equation: Time = dist/speed
:
Time in mts + time on level ground = 7 hrs
{{{111/((s-10))}}} + {{{188/s}}} = 7 
multiply by s(s-10), results:
111s + 188(s-10) = 7s(s-10) 
:
111s + 188s - 1880 = 7s^2 - 70s
:
299s - 1880 = 7s^2 - 70s
Arrange as a quadratic on the right
0 = 7s^2 - 70s - 299s + 1880 
:
7s^2 - 369s + 1880 = 0
You can use the quadratic formula here but this will Factor to: 
(7s - 40)(s - 47) = 0
The reasonable solution:
s = 47 mph on level terrain
:
:
Check solution by finding the times
111/37 = 3 hrs
188/47 = 4 hrs
-------------------
total = 7 hr 
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