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MrRa [10]
1 year ago
14

Yohanne and Mikaela completed a 1-km race. Yohanne finished the race 1 minute after Mikaela. If the speed of Mikaela is 50 meter

s per minute faster than Yohanne's speed, how many minutes did it take Yohanne to finish the race?
Mathematics
1 answer:
lilavasa [31]1 year ago
7 0

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

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