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Question

And express train travels 320 miles between two cities. During the first 70 miles of a trip the train travel through mountainous terrain. The train travel to 14 mph slower through mountainous terrain then through level to rain. If the total time to travel between the two cities was seven hours, find the speed of the train on level to terrain

Answer 1

Speed = distance divided by time driving. The mountainous travel is 70 miles, making the level travel 250 miles. 70/(7-x) = 250/x - 14. Mountainous speed = level speed - 14 mph. Simplify the equation to 14x² - 418x + 1750 = 0. Solve for x using the quadratic formula. 250/x = level speed. 70/(7-x) = mountainous speed. Alternatively, pick an easy number to use, let x=5, then 7-x=2. That's 2 hours in the mountains, 5 hours level travel. So speeds are 70/2=35 mph and 250/5= 50 mph. 50-35=15 mph which is fairly close to the required 14 mph difference. IF you do the tedious calculations correctly, the speeds should come out close to 35 and 50 mph. IF this were a multiple choice test, the correct answer would be the one very close to 35 and 50, and you would not have to take major time doing the calculations. That can be useful for time pressure tests.