a man walking at a constant rate of 5 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 2 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
"when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 2 * 15 / 60 = 1 / 2 miles and the man walks the distance mm , which is 2 * 5 / 60 = 1 / 6 mile . the difference of 1 / 2 - 1 / 6 = 1 / 3 miles ( mw ) will be covered by the man in ( 1 / 3 ) / 5 = 1 / 15 of an hour , which is 4 minutes . answer e ."
multiply(const_60, divide(multiply(divide(2, const_60), subtract(15, 5)), 5))