SOLUTION: A train travelled from A to B and back in a certain time at rate of 60 km/hr. But if the train had travelled from A to B at the rate of 80 km/hr and back from B to A at the rate o

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Question 734373: A train travelled from A to B and back in a certain time at rate of 60 km/hr. But if the train had travelled from A to B at the rate of 80 km/hr and back from B to A at the rate of 40 km/hr it would take 2 hours longer. find the distance between A to B.
Found 5 solutions by lynnlo, ankor@dixie-net.com, ikleyn, greenestamps, josgarithmetic:
Answer by lynnlo(4176)   (Show Source):
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Answer by ankor@dixie-net.com(22740)   (Show Source):
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A train traveled from A to B and back in a certain time at rate of 60 km/hr.
But if the train had traveled from A to B at the rate of 80 km/hr and back
from B to A at the rate of 40 km/hr it would take 2 hours longer.
find the distance between A to B.
:
let d = distance from A to B
let t = time for round trip at 60 km/hr
then
t =
:
"But if the train had traveled from A to B at the rate of 80 km/hr and back from B to A at the rate of 40 km/hr it would take 2 hours longer. "
+ = t + 2
Replace t with 2d/60
+ = + 2
multiply by 240 to clear the denominators, resulting in:
3d + 6d = 4(2d) + 240(2)
9d = 8d + 480
9d - 8d = 480
d = 480 km from A to B
:
:
Confirm this solution by finding the times
960/60 = 16 hrs
and
480/80 = 6 hrs
480/40 = 12 hrs
-------------
total : 18 hr, 2 hrs more

Answer by ikleyn(53354)   (Show Source):
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.
A train travelled from A to B and back in a certain time at rate of 60 km/hr.
But if the train had travelled from A to B at the rate of 80 km/hr and back from B to A at the rate of 40 km/hr
it would take 2 hours longer. find the distance between A to B.
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let 'd' be the distance between A and B, in kilometers. The travel time to move from A to B and back with the constant rate of 60 km/h is hours. The travel time to move from A to B at the rate of 80 km/h and back from B to A at the rate of 40 km/h is + = = hours. The problem says that is 2 hours longer than . So, we write this "time" equation - = 2 hours. (1) It is the setup equation to find 'd'. Multiply all the terms by the common denominator 240. You will get (3d)*3 - (2d)*4 = 2*240 9d - 8d = 480 d = 480. Thus, the distance between A and B is 480 kilometers. ANSWER.

At this point, the problem is solved completely.

This approach using the " time " equation is a universal and powerful method to solve such problems.

Answer by greenestamps(13250)   (Show Source):
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A solution different from the one from the other tutor, using the ratios of the speeds on the two legs of the journey in the two scenarios....

First scenario:
let t be the time for the trip from A to B; then the time for the trip from B to A is also t, for a total time of 2t.

Second scenario:
The trip from A to B is 80/60 = 4/3 times as fast as in the first scenario, so the time for the trip is less by a factor of 4/3; the time for this leg is (3/4)t. The trip from B to A is 40/60 = 2/3 as fast as in the first scenario, so the time for this trip is more by a factor of 3/2; the time for this leg is (3/2)t. The total time for the round trip is (3/4)t + (3/2)t = (9/4)t.

The difference in the times for the two scenarios is (9/4)t - 2t = (1/4)t.

The difference in the times for the two scenarios is 2 hours.

So (1/4)t is 2 hours, which means the time for trip in each direction in the first scenario is 8 hours.

Since the speed in the first scenario is 60 km/hr, the distance between A and B is 60*8 = 480 km.

Answer by josgarithmetic(39681)   (Show Source):
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d is for distance A to B and for B to A.

RATES TIME DISTANCE AS DONE 60 2d/60 2d IF 80 d/80 d 40 d/40 d

If the two other rates then 2 hours longer,
. Solve for d.