Solve the problem.
-An express train travels 186 miles between two cities. During the first 60 miles of a trip, the train traveled through mountainous terrain. The train traveled 12 miles per hour slower through mountainous terrain than
Through level terrain. If the total time to travel between the cities was 5 hours, find the speed of the train on
Level terrain.
A)18 mph
B)54 mph
C)30 mph
D)42 mph

Question

Quizplus · Accepted Answer

Let the speed of the train on level terrain be x mph.

Then, speed of the train through mountainous terrain = (x-12) mph.

Time taken to cover the first 60 miles = 60/(x-12) hours.

Time taken to cover the remaining 126 miles on level terrain = 126/x hours.

Total time taken = 5 hours.

Therefore, 60/(x-12) + 126/x = 5.

Simplifying this equation, we get:

x^2 - 42x + 252 = 0.

Solving for x, we get:

x = 30 or 12.

Since the speed of the train cannot be 12 mph, the only possible answer is 30 mph (choice D). Let x be the speed of the train on level terrain.
The time taken to travel the first 60 miles through mountainous terrain is 60/(x-12).
The time taken to travel the remaining 126 miles on level terrain is 126/x.
The total time taken is 5 hours, so we can set up the equation:
60/(x-12) + 126/x = 5
Multiplying both sides by x(x-12), we get:
60x + 126(x-12) = 5x(x-12)
Simplifying this equation, we get:
186x - 1512 = 5x^2 - 60x
Rearranging and dividing by 5, we get:
x^2 - 49x + 302.4 = 0
Using the quadratic formula, we get:
x = (49 ± sqrt(49^2 - 4*1*302.4))/2*1
x = (49 ± 19.6)/2
x = 34.3 or x = 15.7
Since the train must travel at a speed greater than 12 mph through mountainous terrain, the speed of the train on level terrain is approximately 42 mph (rounded to the nearest whole number). Therefore, the answer is D.

Solve the Problem. -An Express Train Travels 186 Miles Between Two Cities. During