Question 1005772
THE ALGEBRA-STYLE SOLUTION:
{{{L}}}= length of the bridge, in miles
{{{(3/8)*L}}}= distance to cover running towards the train
{{{L-(3/8)*L=(5/8)*L}}}= distance to cover running away from the train
{{{x}}}= the man's running speed, in miles per hour
{{{(3/8)*L/x}}}= time (in hours) the man must run towards the train to save himself
{{{(5/8)*L/x}}}= time (in hours) the man must run away from the train to save himself
Running toward the train is scarier, but it will save time and effort.
The time saved, in hours is
{{{(5/8)*L/x-(3/8)*L/x=(5/8-3/8)*(L/x)=(2/8)*(L/x)=L/"4 x"}}} .
That is the time the train takes to cover the {{{L}}} miles from one end of the bridge to the other, at {{{60}}} miles per hour:
{{{L/60}}} hours.
So,
{{{L/"4 x"=L/60}}}-->{{{1/"4 x"=1/60}}}--->{{{4x=60}}}--->{{{x=60/4}}}--->{{{highlight(x=15)}}} .
 
NOTE:
If you do not need to explain step by step, you can start by writing
{{{(5/8)*L/x-(3/8)*L/x=L/60}}} .
 
ANOTHER WAY TO THINK OF IT:
In the time the man would have run the {{{3/8}}} of the bridge towards the train,
the train will get to the bridge.
During that time, the man can cover another {{{3/8}}} of the bridge,
and be {{{3/8 +3/8=6/8=3/4}}} of the way through the bridge.
While the man runs that remaining {{{1-3/4=1/4}}} of the bridge length,
the train at {{{60}}} miles per hour covers the whole span of the bridge.
Since during the same time the man cover {{{1/4}}} of the distance covered by the train,
his speed must be {{{1/4}}} of the speed of the train, or {{{60mph/4=highlight(15mph)}}} .
That is a mental-math, no-need-to-show-your-work way (the one to use for a quick answer for the SAT).