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# algebra equation from word problem

first train leaves station going 60 mph. 30 minutes later, 2nd train leaves same station going 72 mph. what is equation that tells us how long before 2nd train catches up with 1st train?  We know the answer is 2 hours but don't know equation to show this.

The answer is not 2 hours.

The trains will meet up when the first train has been going for 3 hours and the second train has been going for 2.5 hours. Each will have travelled 180 miles at that point in time.

t is the time that the first train has been traveling in hours.

t-0.5 is the time that the second train has been traveling in hours.

Distance that the first train travels during that time is

t*60

Distance that the second train travels is

(t-0.5)*72

The two trains are at the same distance when those two expressions are equal

t*60 = (t-0.5)*72

60t = 72t-36

36 = 12t

3 = t

I hope that helps.

That should help, Robert, because you laid out all the steps.

The most important thing for this student to learn is that distance - rate*time

and the units must be compatible - minutes or hours on time; distance in miles, let's say; and thus - if hours are used - rate is in miles per hour.

IF they can manage all this, there is no stopping the trains!

[I hope there are two tracks or the secod one runs into the first one!]

Good work.

10/19/2012