There were five runners in this year's Waterfront 10, a ten-mile "out-and-back" race, with a turn-around at the halfway point. Each runner ran their whole race at a constant speed.
Annie reached the 3-mile mark 6 min after the winner, but before at least 1 other runner.
Ben got to the turnaround a full 7 minutes after the third-place runner did.
Carla ran each of the 10 miles of the race in 12 seconds less than 8 minutes.
Dan passed the winner 42 min into the race, then at least 1 other runner before turning around.
Emo had run 5 5/9 miles when he passed the last runner, and had met runners in both directions already.
What was the order of finish, and what was each runner's total ten-mile time, in minutes?
Show your steps and reasoning.
I wrote this while solving, so it includes a couple of errors I made originally; I've marked them and show the corrections at bottom along with the final answer.
Some preliminaries:
Annie's position is somewhere between 2nd and 4th.
Ben was in either 4th or 5th place.
Carla, having run each mile at 7:48, ran the first five miles in 39 minutes, and took 78 minutes to run the full race.
Dan took over 42 minutes to turn around and thus must have been behind Carla. He also came in 3rd, 4th or 5th.
Eno was not the last runner, and also not the first. In fact he was also not second to last, so he was in 2nd or 3rd place.
The order must have been one of the following four:
CEADB
CEABD
CAEDB
CAEBD
As Carla was the winner, the winning time was 78 minutes.
Dan passed Carla 42 minutes into the race, 3 minutes after she had turned around and therefore 3/7.8 miles from the turnaroung point. That's after running 5-3/7.8 miles. That makes a rate of 9.1 minutes per mile, so Dan finished in 91 minutes, 13 minutes after the winner.
Ben finished 14 minutes after the third place finisher did, so Ben must have finished last, making Dan the 4th place finisher.
Emo ran 5+5/9 in the time that Ben ran 5-5/9 miles so his speed was (5+5/9)/(5-5/9) that of Ben. That's 1.25 times the speed, so Ben's time was 1.25 times Emo's time.
Remembering that the order of finish is now either
CEADB or
CAEDB
Annie's time was 78+6 = 84 minutes.
***** This is wrong--a misreading of the clues ****
If Annie was in 3rd place, Ben came in at 91 minutes, but that would tie Dan's time, while I think the implication is there were no ties. So Annie was in 2nd place:
CAEDB
B = E + 14, where B and E are Ben's and Erno's times respectively.
and B = 1.25 * E, so E = 56 minutes and B = 63 minutes.
Carla 78
Annie 84
Emo
Dan
Ben
uh-oh
switching to
CEDAB per revised program for picking possible orders; the first one erroneously disallowed Dan coming in 3rd.
The revised program:
ords=perms('abcde');
for i=1:length(ords)
ord=ords(i,:);
a=find(ord=='a');
b=find(ord=='b');
c=find(ord=='c');
d=find(ord=='d');
e=find(ord=='e');
good=true;
if a<2 || a>4
good=false;
end
if b<4
good=false;
end
if d<3 || d<c % previously had d<4
good=false;
end
if e<2 || e>3
good = false;
end
if good
disp(upper(ord))
end
end
Carla, the winner still had 78 minutes.
Annie has 98 minutes. (corrected the misreading)
Dan had 91 minutes.
Ben finished in 91+14=105 minutes.
Emo used 4/5 of Ben's time, 84 minutes.
In order:
Carla 78
Emo 84
Dan 91
Annie 98
Ben 105
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Posted by Charlie
on 2025-03-10 10:47:26 |
solution
