Question

Bill and Will, starting together, ran a 400-meter race, each running at a constant speed. When Bill crossed the finish line, Will was exactly 20 yards behind Bill. They decide to run the race again, this time Bill starting 20 yards behind the original starting line and each running at his same constant speed as before. This time _______ wins by _______ yards.

Answer 1

Answer: Bill, 1

Step-by-step explanation:

Given

Bill and will run a 400 yard race.

Bill win by 20 yard

Suppose the speed of Bill and Will are $\mathbf{v_b}, \mathbf{v_w}$

time taken for them is same for the first time

$\Rightarrow t_b=t_w\\\\\Rightarrow \dfrac{400}{v_b}=\dfrac{400-20}{v_w}\\\\\Rightarrow \dfrac{v_b}{v_w}=\dfrac{400}{380}\ or\ \dfrac{20}{19}$

Now Bill starts 20 yards behind the starting line

Ratio of their time to cover the distances is

$\Rightarrow \dfrac{t_b}{t_w}=\dfrac{\dfrac{420}{v_b}}{\dfrac{400}{v_w}}\\\\\Rightarrow \dfrac{t_b}{t_w}=\dfrac{420}{400}\times \dfrac{v_w}{v_b}\\\\\Rightarrow \dfrac{t_b}{t_w}=\dfrac{21}{20}\times \dfrac{19}{20}\\\\\Rightarrow \dfrac{t_b}{t_w}=\dfrac{399}{400}$

The obtained ratio is less than 1. Thus, the time taken by Bill is less than Will.

For the same time Bill wins

$\therefore \dfrac{v_b\times t}{v_w\times t}=\dfrac{420}{x}\\\\\Rightarrow x=19\times 21\\\Rightarrow x=399\ m$

Thus, Will has covered only 399 yards.

This time Bill wins by 1 yards.

To learn more visit

https://brainly.in/question/12831056