SOLUTION: Two trains leave a city at the same time. One travels north, and the other travels south 20 mph faster. In 2hr, the trains are 280 mi apart, find their speeds.

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Question 126593: Two trains leave a city at the same time. One travels north, and the other travels south 20 mph faster. In 2hr, the trains are 280 mi apart, find their speeds.
Found 2 solutions by solver91311, marcsam823:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
One train is going mph, and the other is going mph. Since they are travelling in opposite directions, their speed relative to each other is the sum of their speeds, namely:

Using distance = rate times time in the form and plugging in the values we know, we can calculate , the speed of the slower train.

What we know:

So the slower train is going 60 mph, and the faster train is going 60 + 20 = 80 mph.

Check the answer:
One train goes 60 mph for 2 hours so it travels 120 miles. The other train goes 80 mph for the same 2 hours so it travels 160 miles. 120 plus 160 = 280. Answer checks.

Answer by marcsam823(57) (Show Source):
You can put this solution on YOUR website!
For this problem you'll need to remember that rate x time = distance or
We know that both trains travelled a distance that separated them by 280 miles after 2 hours. Therefore:
--The distance travelled by the northbound train (x) plus the distance travelled by the southbound train (y) totals 280 miles or, algebraically:

1. Using our formula we can substitute:
a. Let r = the speed of the northbound train
b. Let = the speed of the southbound train (20 mph faster)
c. Both trains have travelled for 2 hours:
d. Let x =
e. Let y =
2. Substitute for x and y and solve for r:

-The northbound train travels at 60 mph
-The southbound train travels at 80 mph (20 mph faster)
3. Check: