Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading toward station A and train B heading toward station B. Train A reaches station A after 212 h. Train B reaches station B after 4 h. Station A and Station B are 585 mi apart.
What is the rate of the trains?
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mph
To find the rate of the trains, we need to determine the distance each train has traveled.
Train A traveled for 212 hours at a certain rate. Let's call the rate of Train A "r". So, the distance Train A traveled can be calculated as:
Distance = Rate * Time
Distance_A = r * 212
Train B traveled for 4 hours at the same rate. So, the distance Train B traveled can be calculated as:
Distance_B = r * 4
We know that the total distance between the central station and station A is 585 miles. Since Train A is traveling towards station A and Train B is traveling towards station B, the sum of the distances traveled by the two trains should equal 585 miles:
Distance_A + Distance_B = 585
Substituting the expressions for the distances:
(r * 212) + (r * 4) = 585
Simplifying the equation:
212r + 4r = 585
216r = 585
r = 585/216
r ≈ 2.7083
Therefore, the rate of the trains is approximately 2.7083 mph.