Solve the problem.
-An express train travels 356 miles between two cities. During the first 68 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 8 hours, find the speed of the train on
Level terrain.
A) 20 mph
B) 34 mph
C) 48 mph
D) 62 mph

Question

Quizplus · Accepted Answer

Let the speed of the train on level terrain be x mph.
Then, the speed of the train through mountainous terrain is (x - 14) mph.
Using the formula distance = speed × time,
68/(x - 14) + 288/x = 8
Multiplying both sides by x(x - 14), we get
68x + 288(x - 14) = 8x(x - 14)
Expanding and simplifying, we get
8x² - 248x - 3840 = 0
Dividing both sides by 8, we get
x² - 31x - 480 = 0
Factorizing, we get
(x - 48)(x + 17) = 0
Ignoring the negative value, we get x = 48 mph.

Therefore, the answer is C) 48 mph. Let x be the speed of the train through level terrain.
Then the time taken to travel through level terrain is (356-68)/x = 288/x.
The time taken to travel through mountainous terrain is 68/(x-14).
The total time taken is given as 8 hours, so we have the equation:
288/x + 68/(x-14) = 8
Multiplying both sides by x(x-14), we get:
288(x-14) + 68x = 8x(x-14)
Simplifying and rearranging, we get:
8x^2 - 184x + 4032 = 0
Dividing by 8, we get:
x^2 - 23x + 504 = 0
Factoring, we get:
(x-12)(x-42) = 0
Since the speed of the train can't be negative, we have x = 42 mph.
Therefore, the speed of the train on level terrain is 42 mph.

Solve the Problem. -An Express Train Travels 356 Miles Between Two Cities. During