Question 1066637
.
the distance between two villages P and Q is x km . A train running between P and Q arrives 3 minutes behind the scheduled time 
when it travel at an average speed of 45km/h but arrives 9 minutes ahead of the scheduled time when it travels at an average speed of  60km/h,   
(i) calculate distance x
ii) calculate the scheduled time for the journey
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The travel time at the speed of 45 km/h is {{{x/45}}}.

The travel time at the speed of 60 km/h is {{{x/60}}}.

The time at the speed 45 km/h is in 3+9 = 12 minutes longer than at the speed 60 km/h.

It gives you a "time" equation:

{{{x/45 - x/60}}} = {{{1/5}}}.

To solve it, multiply both sides by 180. You will get

4x - 3x = 36.

x = 36.

Thus you just found the distance. It is 36 kilometers.


The time spent at the speed of 45 km/h was {{{36/45}}} = {{{4/5}}} of an hour = 48 minutes.

It was in 3 minutes longer than the scheduled time.
Hence, the scheduled time is 48-3 = 45 minutes.
</pre>

All question are answered. The problem is solved.


For similar solved problems see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/How-far-do-you-live-from-school.lesson>How far do you live from school?</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Travel and distance</U>".