A can beat B by 20 yards in a race of 200 yards. B can beat C by 10 yards in a race of 250 yards. By how many yards can A beat C in a race of 100 yards?
Hello, hisajesh!
A can beat B by 20 yards in a 200-yard race.
B can beat C by 10 yards in a 250-yard race.
By how many yards can A beat C in a 100-yard race?
Let
In the time A has run 200 yards, B has run only 180 yards.
B's speed is of A's speed: . .[1]
In the time B gas run 250 yards, C has run only 240 yards.
C's speed is of B's speed: . .[2]
Substitute [1] into [2]: .
. . That is, C's speed is of A's speed.
When A has run 100 yards, C has run only yards.
Therefore, A wins by yards.