Question 3173: A train leaves a station and travels west at 54mph. Four hours later, a second train leaves the same station and travels west at 90mph. When will the second train overtake the first?
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! Amberlemon's work is very wrong. Ignore it. Just by looking at the solution...after 8 hours, train 1 will have gone 54*8=432miles. In 4 hours, train2 will have gone 90*4=360miles.
Besides this, the structure of the basic equations are so wrong. Anyway, here is a correct solution:
Definitions:
Let s = speed of train
Let d = distance travelled
Let t = time travelled by first train
Let T = time travelled by second train.
Formula relating these is s = d/t or s=d/T
Now, for train1: 54 = d/t and train2: 90 = d/T... both have the same distance d, since we want to find the time when they meet, ie have travelled the same distance.
We can re-arrange these to give:
54t = d and
90T = d
Since both have d, we can equate the 2 equations and say that 54t = 90T.
How about relating t and T?, well, we know that T = t-4, so put this into the second equation.
54t = 90(t-4)
54t = 90t - 360
36t = 360
so t=10 hours.
So train 2 will take over the first when train1 has been travelling for 10 hours. Or when train2 has been travelling for (10-4) --> 6hours.
Check: in 10 hours, train1 (10*54) --> travels 540 miles.
in 6 hours, train2 travels ( 6*90) --> 540 miles.
jon
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