SOLUTION: Suppose two trains leave a station at the same​ time, traveling in opposite directions. Train B travels 20 mph faster than Train A. In 3.5 ​hours, the trains are 364 miles apar

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Question 1197743: Suppose two trains leave a station at the same​ time, traveling in opposite directions. Train B travels 20 mph faster than Train A. In 3.5 ​hours, the trains are 364 miles apart. Find the speed of each train.
Found 2 solutions by Shin123, math_tutor2020:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the speed of Train A. Then, x%2B20 is the speed of Train B. In 3.5 hours, Train A traveled 3.5x miles, and Train B traveled 3.5%28x%2B20%29=3.5x%2B70 miles. Since they are traveling in opposite directions, the total distance apart is 3.5x%2B%283.5x%2B70%29=7x%2B70. Since we know they are 364 miles apart, we have the equation 7x%2B70=364. Subtracting 70 from both sides, we get 7x=294. Dividing both sides by 7, we get x=42. Therefore, Train A is traveling at 42 mph, and Train B is traveling at 42+20=62 mph.

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Let's define three points on a map as P,Q,R
P = location where train A ends up after 3.5 hours.
Q = starting point of both trains.
R = location where train B ends up after 3.5 hours.
I'll have these points all on the same horizontal line. See the diagram below.

Train A starts at Q and ends up at P.
It travels west at some speed x for 3.5 hours
It covers a distance of 3.5x miles
Use the formula: distance = rate*time

Train B starts at Q and ends up at R.
It travels east at some speed x+20, i.e. 20 mph faster compared to train A, for 3.5 hours.
It covers a distance of 3.5(x+20) = 3.5x+70 miles
This is the length of segment QR.

This is what the diagram looks like

The pieces PQ and QR add up to the whole thing PR, which spans 364 miles.

PQ + QR = PR
(3.5x) + (3.5x+70) = 364
7x+70 = 364
7x = 364-70
7x = 294
x = 294/7
x = 42
Train A travels at 42 mph.
Train B travels at x+20 = 42+20 = 62 mph.