1955 AHSME Problems/Problem 50
Solution
Let be
's velocity, respectively. We want to pass
before we collide with
. Since
and
are going in the same direction and
,
will pass
in
time. Since
and
are going in opposite directions, their velocity is given by
, so the amount of time before
will collide with
is given by
. We want to pass
before we collide with
, so
must satisfy the inequality
. We can eliminate all the units, simplifying the inequality to
. Solving this and substituting our known values of
and
yields
, so
must increase his speed by
miles per hour.
~anduran