Can't get the second winner of a race, I only can get the winner

This code attempts to find the winner of a race and the second position by taking the player who put less time to complete the race.

#include <stdio.h>

int main(){
    unsigned int choice;
    int id[8] = {0};
    float time[8] = {0};
    for(size_t i=0; i<8; ++i) {
        printf("\nWrite id player: ");
        scanf("%d", &(id[i]));
        printf("\nWrite time: ");
        scanf("%f", &(time[i]));
    }
    size_t num1 = 0;
    size_t num2 = 0;
    for(size_t j=0; j<8; ++j){
        if (time[num1]>time[j]){
            num1 = j;       // to find the winner
        }
        if (time[num2]>time[j] && time[num2]>time[num1]){
            num2 = j;       // to find the second position player
        }
    }

    printf("\n\nWinner: %d, with time: %f", id[num1], time[num1]);
    printf("\n\nSecond: %d, with time: %f", id[num2], time[num2]);
    printf("\n\n");
}

Can't get why this doesn't work, it works only for the winner, but doesn't work for the second position player.

Output:

Write id player: 1838

Write time: 4

Write id player: 3492

Write time: 6

Write id player: 3219 

Write time: 2

Write id player: 48929

Write time: 9

Write id player: 38928

Write time: 4

Write id player: 23892

Write time: 4

Write id player: 89498

Write time: 1

Write id player: 48929

Write time: 6


Winner: 89498, with time: 1.000000

Second: 89498, with time: 1.000000

Shouldn't the time[num2]>time[j] && time[num2]>time[num1] condition do the job? Shouldn't the &&make sure that the time of the second winner is yes minor of the j-th, but also greater than the winner.