Question

Twenty-eight athletes participate in a 100-meter race. The time of each athlete is measured during the qualification round. The average time is 11 seconds. The 8 athletes with the fastest time qualified for the final. The average time of these 8 athletes is 10.5 seconds. Calculate the average time of the 20 athletes who did not qualify for the final.

Answer 1

The average time of the 20 athletes who did not qualify for the final is 11.2 seconds .

Step-by-step explanation:

Here we have , Twenty-eight athletes participate in a 100-meter race. The time of each athlete is measured during the qualification round. The average time is 11 seconds. The 8 athletes with the fastest time qualified for the final. The average time of these 8 athletes is 10.5 seconds. Let's have equations for this:

$\frac{x_1+x_2+.....+x_2_8}{28} = 11$ where $x_1, x_2, ....., x_2_8$ are athletes

⇒ $x_1 + x_2 + .. + x_2_8 = 11(28)= 308$

⇒ $(x_1 + x_2 + .. + x_8 )+ (x_9+x_1_0+...+x_2_8) = 308$

⇒ $(\frac{x_1 + x_2 + .. + x_8}{8} )(8)+ (\frac{x_9+x_1_0+...+x_2_8}{20} )(20) = 308$

⇒ $10.5(8)+m(20) = 308$ , where m is average time of the 20 athletes who did not qualify for the final.

⇒ $84+m(20) = 308$

⇒ $20m= 224$

⇒ $m=11.2$

∴ The average time of the 20 athletes who did not qualify for the final is 11.2 seconds .