Question

At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

A number line goes from 0 to 25. A line is drawn from 3 to 25. The point at 3 is labeled Start and the point at 25 is labeled End.



Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4.

4.4 meters
7.4 meters
17.6 meters
20.6 meters

Answer 1

Let x be Ario’s position in meters from the 0 end. Completed = x − 3, remaining = 25 − x.
Set (x − 3)/(25 − x) = 1/4.

Solve: 4(x − 3) = 25 − x → 4x − 12 = 25 − x → 5x = 37 → x = 7.4.

So Ario will be at 7.4 meters.