SOLUTION: an express train travels 343 miles between two cities. during the first 78 miles of a trip, the train traveled through mountainous terrain. the train traveled 14 miles per hour slo
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Question 370864: an express train travels 343 miles between two cities. during the first 78 miles of a trip, the train traveled through mountainous terrain. the train traveled 14 miles per hour slower through mountainous terrain than through level terrain. if the total time to travel between the cities was 7 hours, find the speed of the train in level terrain Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! an express train travels 343 miles between two cities.
during the first 78 miles of a trip, the train traveled through mountainous terrain.
the train traveled 14 miles per hour slower through mountainous terrain than
through level terrain.
if the total time to travel between the cities was 7 hours,
find the speed of the train in level terrain
:
Let s = train speed in level terrain
then
(s-14) = speed in the mountains
:
Find the distance on level terrain: 343 - 78 = 265 mi
:
Write a time equation; Time = dist/speed
:
Time in mtns + level time = 7 hrs + = 7
:
Multiply by s(s-14), results:
78s + 265(s-14) = 7s(s-14)
:
78s + 265s - 3710 = 7s^2 - 98s
:
343s - 3710 = 7s^2 - 98s
:
Arrange as quadratic equation
7s^2 - 98s - 343s + 3710 = 0
7s^2 - 441s + 3710 = 0
:
Simplify, divide by 7
s^2 - 63s + 530 = 0
:
You can use the quadratic formula but this will factor to:
(s-10)(s-53) = 0
Two solutions
s = 10
and
s = 53; this is the only reasonable solution
:
53 mph on level terrain (39 mph in the mountains)
:
:
Check by finding the times at each speed
78/39 = 2 hrs
265/53 = 5 hrs
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totals: 7 hrs
