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let's start by listing all the givens.
total distance is 420 miles.
slower train goes at 45 mph
faster train goes at 60 mph.
the formula for distance is d=rt.the faster train's rate is 60 mph. we don't know how much distance that train will cover, therefore, we should give it a variable, such as d (any letter)the slower train's rate is 45 mph. obviously, it will cover much less distance than the faster train. so we can write it as (the variable here should match the one above.we don't know the time it will consume for both of the trains so we can give it a variable like .
let's look at the given for the faster train. d (distance, unknown), 60 (rate), and t (time, unknown). using the formula d=rt. we can substitute 60 to the rate to make it . sure you might not able to solve it at hindsight, but we could substitute it to the slower train's equation.
now, the equation for the slower train is ( is the distance, 45 is the rate, and t is the time.)substute 60t to d: bring 60t to the other side by means of adding 60t to both sides: ==> divide 105 to both sides to isolate t:
so if t = 4, it means the trains must travel 4 hours (because of miles per hour) before they meet
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