what is the number of runners in the race?

Question

jason placed exactly in the middle among all the runners in a race. bob was a little slower than jason, in 10th place, and harry was in 16th place. what is the number of runners in the race? 

Answer 1

Hi Baily,

 

here's what I got that Bob is 10 place and that Jason is ahead of him => Jason < 10

 

That Harry is 16th place => That the total has to be at least 17

 

=> That the number has to be 9.  1,2,3,4,5,6,8 people ahead of the median (Jason) and 10,11,12,13,14,15,16,16, another 8 people behind the median.

 

I hope this helps

Answer 2

Hi Bailey--

 

Let's assume that " a little slower" means that Bob was right after Jason, which means Jason was in 9th place. That would mean that 8 finished ahead of him, and therefore 8 also finished after him.

 

It would look like this, with Jason being the orange 9 in the middle, with 8 runners on either side.

 

1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17

 

As far as I can tell, the information about Harry doesn't matter, except to maybe give us a hint that there were at least 16 runners in the race.

 

Hope this helps!

 

Matt in New York

Answer 3

We can't answer exactly, but if we make a few assumptions there is a solution

Let's assume that "a little slower that Jason" means that Bob finish immediately after Jason.

That means the Jason finished 9th. Since Jason finished in the middle, 8 people finished ahead of Jason and 8 people finished behind him. So, we have 8 + 1(Jason) + 8 = 17 people in the race.