1955 AHSME Problems/Problem 50
In order to pass going mph on a two-lane highway, , going mph, must gain feet. Meantime, feet from , is headed toward him at mph. If and maintain their speeds, then, in order to pass safely, must increase his speed by:
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 relative velocity is , 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