Se   B   H   S   R    Total
   |============================
 B |                        24
 M |
 Ja|
 R |
 Jo|             5   3

The only possible points for Ben achieving 24 is { 5 5 5 5 4 } and since Joel got first in the skateboard race (5 points), we know that is where Ben's 4 comes from.

We also know that the total number of points given out was 75. (5 * (5 + 4 + 3 + 2 + 1))

Joel had to have at least 11 points. If Joel had more than 11 points, say 12, then is it possible to achieve a solution? Ruth would have had to have at least 13 (since there were no ties), and Jason 14, and Mark 15. That would yield an overall total of 78. Too much! So Joel definitely had 11 points.

    Se   B   H   S   R    Total
   |============================
 B | 5   5   5   4   5      24
 M |
 Ja|
 R |
 Jo| 1   1   1   5   3      11

Using the same logic as before, we also know that Ruth could not have gotten more than 12 points. If she had 13, and Jason 14, and Mark 15, the total would be 77. Still too much. So Ruth had 12, and continuing on by looking at the final rankings, Jason had to have 13 and Mark 15, otherwise the totals would be over 75.

Now we know Jason had 13 points. If he got four 4's for consistency, it wouldn't work (already over 16). If he got four 2's, it also wouldn't work (8 points plus the maximum 4 is still only 12 -- all the fives are already taken). So he had to have received four 3's, and since he couldn't have gotten a 3 from the roller skate race, that is where he received a 1.

    Se   B   H   S   R    Total
   |============================
 B | 5   5   5   4   5      24
 M |                        15
 Ja| 3   3   3   3   1      13
 R |                        12
 Jo| 1   1   1   5   3      11

Let's look at Ruth. We can see from the chart that all 5's and 3's have already been given out (and there is only one 1 left). So Ruth's scores can only contain 4's, 2's, or a single 1. Given that information the only possible combination of 5 scores that would yield 12 is { 2 2 2 2 4 }. Since Ben already has a 4 from the skateboard race, Ruth must have a 2 there.

    Se   B   H   S   R    Total
   |============================
 B | 5   5   5   4   5      24
 M |                        15
 Ja| 3   3   3   3   1      13
 R |             2          12
 Jo| 1   1   1   5   3      11

Hence Mark must have gotten 1 point in the skateboard race, so Mark came in last place in the skateboard race!

    Se   B   H   S   R    Total
   |============================
 B | 5   5   5   4   5      24
 M |             1          15
 Ja| 3   3   3   3   1      13
 R |             2          12
 Jo| 1   1   1   5   3      11