SOLUTION: A train travels a certain journey and is supposed to arrive at midday. When its average speed is 40km/h, it arrives at 1 p.m. When its average speed is 48km/h, it arrives at 11 a.m

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Question 1207036: A train travels a certain journey and is supposed to arrive at midday. When its average speed is 40km/h, it arrives at 1 p.m. When its average speed is 48km/h, it arrives at 11 a.m. What is the length of the journey?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A train travels a certain journey and is supposed to arrive at midday.
When its average speed is 40km/h, it arrives at 1 p.m.
When its average speed is 48km/h, it arrives at 11 a.m.
What is the length of the journey?
~~~~~~~~~~~~~~~~~~~~ 

Let "d" be the length of the journey.


Then the travel time in the first  scenario was    hours.

     The travel time in the second scenario was    hours.


The difference between these two travel times was 2 hours (from 11 am to 1 pm).

So, we write this time equation

     -  = 2  hours.


To solve it, multiply both sides by 240.  You will get

    6d - 5d = 2*240

       d    = 480.


ANSWER.  The length of the journey is 480 kilometers.

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Let x be the number of hours the trip takes at 48km/hr.

Then, since the arrival time at the lower speed is 2 hours later, x+2 is the number of hours it takes at 40km/hr.

The distances at the two speeds are the same:

48(x) = 40(x+2)
48x = 40x+80
8x = 80
x = 10

The trip at 48km/hr takes 10 hours, so the distance is 48*10 = 480km.

ANSWER: 480km

Here is a quick informal way to solve the problem mentally, if your mental math is good....

The ratio of the two speeds, as a fraction, is 40/48.

The distances are the same, so the ratio of the times is the same as the ratio of the speeds.

Since the difference in the times is 2 hours, write the ratio 40/48 as an equivalent fraction in which the difference between the numerator and denominator is 2: 40/48 = 10/12.

So the trip takes 12 hours at 40km/hr or 10 hours at 48km/hr, making the trip 480km.
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