A train leaves a station and travels west at 54mph Four hour

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?

Solution

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.