UNO High School Problem of the Week Competition
Problem 8
In a ten-mile race First beats Second by 2 miles and First beats Third by 4 miles. If the runners maintain constant speeds throughout the race, by how many miles does Second beat Thirds.
Solution
From the given information the ratio of the distances covered by First, Second and Third, in that order is 10:8:6. Since speeds remain constand the ratio of the distances remains constant, so that, when Second completes an additional 2 miles, Third completes an additiona 1 1/2 miles since 2/x = 8/6 where x is the additional distance completed by Third. Therefore, when Second completes 10 miles, Third completes 7 1/2 miles, that is Second beats Third by 2 1/2 miles.
