Question 1071054
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Let "r" be the rate of the passenger train, in mph.

Then the rate of the freight train is (r-15) mph.

The time the passenger train spent for 180 miles trip was {{{180/r}}} hours.

The time the freight train spent for 120 miles trip was {{{180/(r-1)}}} hours.


The condition says that these two amounts of times are equal:


{{{180/r}}} = {{{120/(r-15)}}}   ("A passenger train traveled 180 miles in the same amount of time it took a freight train to travel 120 miles.")


Solve this equation. For it, multiply both sides by r*(r-15). You will get

180*(r-15) = 120r  --->  180r - 2700 = 120 r  --->  180r - 120 r = 2700  --->  60r = 2700  --->  r = {{{2700/60}}} = 45.


<U>Answer</U>. The passenger train rate is 45 mph. That for the freight train is 30 mph.
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Solved.