Question

Yohanne and Mikaela completed a 1-km race. Yohanne finished the race 1 minute after Mikaela. If the speed of Mikaela is 50 meters per minute faster than Yohanne's speed, how many minutes did it take Yohanne to finish the race?

Answer 1

Answer: 5 min

Step-by-step explanation:

Given

Length of the race track $l=1\ km\ or\ 1000\ m$

Suppose the speed of Yohanne is $v_y=x\ m/min.$

then  Mikaela speed is $v_m=50+x$

the difference in the finishing time is 1 minute i.e.

$\Rightarrow \dfrac{1000}{x}-\dfrac{1000}{50+x}=1\\\\\Rightarrow \dfrac{50+x-x}{x(50+x)}=\dfrac{1}{1000}\\\\\Rightarrow \dfrac{50}{x(50+x)}=\dfrac{1}{1000}\\\\\Rightarrow x^2+50x-50,000=0\\\\\Rightarrow x^2+250x-200x-50,000=0\\\\\Rightarrow (x+250)(x-200)=0\\\\\Rightarrow x=200\ m/min.$

Time taken by Yohanne is

$\Rightarrow t=\frac{1000}{200}=5\ min$