Question 734373
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 = {{{(2d)/60}}}
:
"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. "
{{{d/80}}} + {{{d/40}}} = t + 2
Replace t with 2d/60
{{{d/80}}} + {{{d/40}}} = {{{(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
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total : 18 hr, 2 hrs more