A freight train leave A for B 175 miles away and travels at the rate or 31.5
mph. after 1.5 hours a train leaves B for A traveling at 21.5 mph. How many
miles from B will they meet?
Distance = rate×time. Therefore:
When the train leaves B, the train that left A is already (31.5)(1.5) or
47.25 miles down the track toward B, so they are only 175-47.25 or 127.75 miles
apart then.
Their approach rate is the sum of their rates or 31.5+21.5 or 53 mph.
Since 
, they will meet 
hours after the train that left B started.
So, since 
, it will have traveled 21.5× or
51.82311321 miles from B.
Checking: The train that left A will have traveled an additional
31.5× miles or 75.92688679 miles and when we add those
we get 127.75 miles.
Answer: 51.8 miles approximately
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Here is another way to solve it. Make this chart, filling in the
rates:
distance rate time
train leaving A 31.5
train leaving B 21.5
Let the time traveled by the train that left B be t.
Then the train that left A will have traveled t+1.5
distance rate time
train leaving A 31.5 t+1.5
train leaving B 21.5 t
Fill in the distances using distance = rate×time
distance rate time
train leaving A 31.5(t+1.5) 31.5 t+1.5
train leaving B 21.5t 21.5 t
The sum of the distances must equal 175, so
31.5(t+1.5) + 21.5t = 175
31.5t + 47.25 + 21.5t = 175
53t + 47.25 = 175
53t = 127.75
t =
t = 2.410377358 hours
The answer is the distance traveled by the train leaving B.
21.5t = 21.5(2.410377358) = 51.8231132 miles.
Edwin
