Question 891545
You can think of this as one of the trains
moving at either the sum or the difference
of their speeds, and the other train standing
still.
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Let {{{ s[1] }}} = the speed of the faster train
Let {{{ s[2] }}} = the speed of the slower train
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Trains traveling in opposite directions:
(1) {{{ 220 + 180 = ( s[1] + s[2] )*16 }}}
Trains traveling in same direction:
(2) {{{ 220 + 180 = ( s[1] - s[2] )*60 }}}
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In both cases, the length of one train has to 
completely pass the length of the other, so
you add the lengths.
It takes longer to pass going in the same 
direction, so you subtract the speeds
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(1) {{{ 400 /16 = s[1] + s[2] }}}
(1) {{{ s[1] + s[2] = 25 }}}
and
(2) {{{ 400/60 = s[1] - s[2] }}}
(2) {{{ s[1] - s[2] = 20/3 }}}
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Add the equations
{{{ 2s[1] = 95/3 }}}
{{{ s[1] = 95/6 }}}
{{{ s[1] = 15.833 }}}
and
(2) {{{ s[1] - s[2] = 20/3 }}}
(2) {{{ 95/6 - s[2] = 40/6 }}}
(2) {{{ s[2] = 55/6 }}}
(2) {{{ s[2] = 9.166 }}}
The speeds of the trains are 15.833 m/sec
and 9.166 m/sec
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check:
(1) {{{ 400 /16 = s[1] + s[2] }}}
(1) {{{ 400 /16 = 15.833 + 9.166 }}}
(1) {{{ 25 = 25 }}}
and
(2) {{{ s[1] - s[2] = 20/3 }}}
(2) {{{ 15.833 - 9.166 = 6.666 }}}
(2) {{{ 6.666 = 6.666 }}}
OK