Answer: [tex]31\dfrac{7}{12}\text{ minutes}[/tex]
Step-by-step explanation:
Given: Time taken by third-place finisher = [tex]34\dfrac23[/tex] minutes
Time taken by second-place finisher =(Time taken by third-place finisher ) - [tex]1\dfrac34[/tex] minutes
= [tex]34\dfrac23-1\dfrac{3}{4}[/tex]
[tex]=\dfrac{104}{3}-\dfrac{7}{4}\\\\=\dfrac{4(104)-7(3)}{12}\\\\=\dfrac{395}{12}\text{ minutes}[/tex]
Time taken by first finisher = Time taken by second-place finisher ) - [tex]1\dfrac13[/tex] minutes
[tex]=\dfrac{395}{12}-\dfrac{4}{3}\\\\=\dfrac{395}{12}-\dfrac{4\times4}{3\times4}\\\\=\dfrac{395-16}{12}\\\\=\dfrac{379}{12}\\\\=31\dfrac{7}{12}\text{ minutes}[/tex]
Time taken by first finisher [tex]=31\dfrac{7}{12}\text{ minutes}[/tex]
