Question 1163985
There are two cities, A, and B. A fast train can go from A to B in 8 hours.
 A slow train can go from B to A in 12 hours.
 They start from the two cities toward each other at the same time.
 when they met, the fast train went 192 km more than the slow train.
 How far is it from A and B?
:
let x = the distance traveled by the slow train to the meeting point
then
(x+192) = the distance traveled by the fast train to the meeting point
and
(2x+192) = the distance from A to B
:
An inverse relationship between the distance and the travel times from A to B
{{{(x+192)/x)}}} = {{{12/8}}}
12x = 8(x+192)
12x = 8x + 1536
12x - 8x = 1536
4x = 1536
x = 1536/4
x = 1536/4
x = 384 km from B to the meeting point
then
192+384 = 576 km from A to the meeting point
and
384 + 576 = 960 km from A to B
:
:
:
Check; find the actual speed of each
960/8 = 120 km/hr, the fast train
960/12 = 80 km/hr, the slow
:
Find the times to the meeting point, should be equal
576/120 = 4.8 hrs
384/80 = 4.8 hrs