Question 768640
How far does #12 get in 12 min?
{{{ d[1] = 55*(12/60) }}} ( I converted 12 min to hrs )
{{{ d[1] = 55*(1/5) }}}
{{{ d[1] = 11 }}} mi
The trains are now {{{ 15.5 - 11 = 4.5 }}} mi apart
----------------
Start a stopwatch when #7 leaves
Let {{{ t }}} = time ( in hrs ) on stopwatch when they meet
Let {{{ d[7] }}} = distance #7 has to travel until they meet
----------------
#7's equation:
(1) {{{ d[7] = 35t }}}
#12's equation:
(2) {{{ 4.5 - d[7] = 55t }}}
-------------------
Substitute (1) into (2)
(2) {{{ 4.5 - 35t = 55t }}}
(2) {{{ 90t = 4.5 }}}
(2) {{{ t = .05 }}} hrs
------------------
(1) {{{ d[7] = 35*.05 }}}
(1) {{{ d[7] = 1.75 }}} mi
-----------------
To find how far #12 is from where it started,
add it's head start to distance after the
stopwatch was started
{{{ d[12] = 11 + ( 4.5 - d ) }}}
{{{ d[12] = 11 + 4.5 - 1.75 }}}
{{{ d[12] = 13.75 }}}
-----------------
#12 is 13.75 mi from the downtown station
-----------------
#12 has been traveling for the 11 min head start plus {{{ t }}}
{{{ t[12] = 11 + .05*60 }}} ( convert hrs to min )
{{{ t[12] = 11 + 3 }}}
{{{ t[12] = 14 }}}
--------------
#12 has been traveling for 14 min