Question

In a race, the second-place finisher crossed the finish line 1 1 3 minutes after the first-place finisher. The third-place finisher was 1 3 4 minutes behind the second-place finisher. The third-place finisher took 34 2 3 minutes. How long did the first-place finisher take?

Answer 1

Answer:
`31(7)/(12)\text{ minutes}`

Explanation:

Given: Time taken by third-place finisher =
`34\frac23` minutes

Time taken by second-place finisher =(Time taken by third-place finisher ) -
`1\frac34` minutes

=
`34\frac23-1(3)/(4)`

`=(104)/(3)-(7)/(4)\\\\=(4(104)-7(3))/(12)\\\\=(395)/(12)\text{ minutes}`

Time taken by first finisher = Time taken by second-place finisher ) -
`1\frac13` minutes

`=(395)/(12)-(4)/(3)\\\\=(395)/(12)-(4*4)/(3*4)\\\\=(395-16)/(12)\\\\=(379)/(12)\\\\=31(7)/(12)\text{ minutes}`

Time taken by first finisher
`=31(7)/(12)\text{ minutes}`