Help plz

From Rick's point of view and speed, D**k is 1/2 hour, or 4.5 km behind him. Since Rick is running at 9 km/h, that means that D**k has to cover a distance of 18 + 4.5=22.5 km in 2 hours=22.5/2=11.25 km/h. So, to finish first, D**k must, ever so slighly, exceed this average.

Mmmmm...I'm not sure about Guest's answer.....it could be correct......but consider

It will take Rick 18km/ [9k//hr]  = 2 hours to finish  

And runnining at his current pace, it will take D**k 2.5 hours to finish

But...he needs to cut this to 2 hours just to finish even with Rick

Call his normal rate per hour, R  and call his increased rate in order to catch Rick, (R + x)

And since R * T  = D.......we have this situation......

At his current rate, the distance he has left to run = R *2.5

And at  his his increased rate, the distance he has left to  run is the same....and this is given by:

(R + x)*2  = D     .....so.....equating the distance, we have......

R * 2.5  =  (R + x) * 2    simplify

2.5R  = 2R + 2x       subtract 2R from both sides

.5R  = 2x      divide both sides by 2

.25R   = x 

So.....he needs to run (R + .25R)    = 1.25R   = 5/4 his current rate just to tie Rick   

Consider this in light of the Guest's answer.......if 5/4  of D**k's current rate = 11.25km/hr, then his current rate must  just be 4/5 of this......but 4/5 of this = 9km/hr......the very same rate that Rick runs.....and if D**k runs at the same rate as Rick, he would be even with him, not 30 minutes behind....!!!

In my opinion.....we actually can't provide an exact numerical answer to this because we would have to know how far D**k has run and the time he has taken to do so to get his current rate.....

I may have blown a fuse, here......can some other mathematician look at  this   ????

Rick is in first place 18 km from the finish.

D**k is 30 minutes behind Rick  

If Rick averages 9 km an hour, how fast does D**k have to average to win?

Hi Chris, maybe you did b**w a fuse LOL

As Chris said, Rick will run 18 km at 9km/hour so that will take him 2 hours.  

D**k is a half hour behind.

It will take him 0.5 hours to get to where Rick was then he has to finish in under 1.5 hours in order to catch up to Rick.

So D**k will need to run the 18km in 1.5 hours   

18 divided by 1.5 = 27km/hour  

So D**k will need to be running fast than an average of 12 km/hour to win the race. 

If the two runners started together and d**k runs slower until he got half hour behind Rick  and then D**k decided to suddenly speed up then it will take him less than 30 minutes to catch up to where Rick is now.

If D**k was travelling at     x km/hour   and at that pace he is a half hour behind Rick, then he will have 0.5x km till he gets to where Rick is.

So D**k needs to go faster than (18+0.5x) km in 2 hours

that is D**k needs to run faster than           (9+0.25x) km/hour

We need more information if you want to work our what x is.

One final note on this one.....apparently.....there isn't exactly a consensus of opinion about what the correct answer may be. As Melody stated, I have assumed that each person started at the same time and that D**k runs at a slower pace than Rick.....

One problem???   The statement that D**k is "30 minutes" behind Rick.....but.....from whose point of view does the "30 minutes" refer???  If it's from Rick's frame of reference, he would be farther ahead than if it was from D**k's frame of reference, given my assumption that Rick runs faster than D**k.......

Whatever.........this actually might be a very good problem if there were a little more info included.