Question 1035059
.
Train T leaves the station at 10 am.  Twenty minutes later, Train G leaves the same station heading in the same direction as Train T.  
Train T travels at 50 mph while Train G travels at 60 mph.  
How long, what time and how far are the trains from the station when Train G catches up Train T?
I know d=rt, r=d/t and that t=d/r but I'm truly stuck on this one.
Thank you so much.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
In 20 minutes after train T started, it will be at the distance {{{(1/3)*50}}} miles from the station.

( {{{1/3}}} is {{{1/3}}} of an hour, or 20 minutes! )

Let "t" be the time measured after 10:20 am, when both train are running till the moment when the train G catches up the train T.

During this time "t" the train T covers the distance 50*t miles (so, you use the formula d = rt just in the second time).

During this time "t"the train G covers the distance 60*t miles (so, you use the formula d = rt just in the third time).

But the distance covered during the time "t" by the train G is by the value of {{{(1/3)*50}}} longer than that covered 
by the train T during the same time "t". It gives you an equation

60*t = 50*t + {{{(1/3)*50}}}.

To solve it, multiply both side by 3. You will get

180t = 150t + 50,

180t - 150t = 50,

30t = 50, 

t = {{{50/30}}} = {{{5/3}}} hour = 100 minutes = 1 hour and 40 minutes.

So, the train G will catch the train T in 1 hour and 40 minutes, counting from 10:20 am. 
In other words, the train G will catch the train T at noon, 12:00. 


During 1 hour and 40 minutes (={{{5/3}}} hour) the train G will cover {{{60*(5/3)}}} = 100 miles.

So, the train G will catch the train T in 100 miles from the station.


Did I answered all your questions?
</pre>

See the lesson <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems.lesson>Travel and Distance problems</A> in this site and many other lessons on Travel and Distance, associated with it.