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) About Me  (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?
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Let "d" be the length of the journey.


Then the travel time in the first  scenario was  d%2F40  hours.

     The travel time in the second scenario was  d%2F48  hours.


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

So, we write this time equation

    d%2F40 - d%2F48 = 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) About Me  (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.