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

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 (1000)/(x)-(1000)/(50+x)=1\\\\\Rightarrow (50+x-x)/(x(50+x))=(1)/(1000)\\\\\Rightarrow (50)/(x(50+x))=(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=(1000)/(200)=5\ min`