bonanova Posted October 2, 2008 Report Share Posted October 2, 2008 It's algebra night, me lads, Alex intoned as he set an empty mug on his fav table at Morty's last night. And you might want to bring a pencil along, this one is a wee bit complicated. Ian was home sick, so that left Davey and Jamie to humor Alex. Pencils are ready, they said, shoot! So, Alex Jr. and I took a trip the other day, one of us on our horse, the other in our car. After a while, I observed that if I had gone three times as far as I had, I would have half as far to go as I had; and if Jr. had gone half as far as he had, he would have three times as far to go as he had. By the way, we started at the same time and place, and were headed for the same destination. Did you get all that? They nodded, but Davey was stroking his beard just a little more vigorously than usual. OK, they said, but ... what's the question? The question, lads is this: which one of us rode the horse? It took Davey only a minute to answer. I think I know... Do you? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 2, 2008 Report Share Posted October 2, 2008 Let Alex be at a distance x and Alex Jr. at y. Let total distance be z. Then 1. 3x + 3x/2 = z => x = 2z/9 2. y/2 + 3y/2 =z => y = z/2 Therefore assuming car is faster than the horse Jr. is on car Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 2, 2008 Report Share Posted October 2, 2008 Jr is driving the car We have two equations, where S is the distance Alex Sr. traveled, J is the distance Alex Jr traveled, and D is the total distance to be traveled: 1/2(D-S)=D-3S (D-1/2J)=3(D-J) Solving, this gives S=1/5D and J=4/5D Since Jr. traveled 4 times the distance in the same amount of time, he must be driving the car. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 2, 2008 Report Share Posted October 2, 2008 It should be Jr... Since would have less distance left Quote Link to comment Share on other sites More sharing options...
0 preflop Posted October 2, 2008 Report Share Posted October 2, 2008 this one is tough Jr was on the horse, pulling Alex in the car. Quote Link to comment Share on other sites More sharing options...
0 k-man Posted October 2, 2008 Report Share Posted October 2, 2008 Jr travelled 4/5 of the way, while you only covered 1/5, so you must've been riding a horse Quote Link to comment Share on other sites More sharing options...
0 Prime Posted October 2, 2008 Report Share Posted October 2, 2008 The way I see it...The way I see it: Alex Sr. traveled 2/9 of his distance, Alex Jr. 2/7 of his. Alex Sr. was driving his car along the road where the distance to the destination was 90 miles. Alex Jr. was riding the horse on the trail, which cut across the canyon with the total trail length 28 miles to the destination. Alex Sr. drove for half an hour at 40 mph, Alex Jr. rode for half an hour at 16 mph. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted October 2, 2008 Author Report Share Posted October 2, 2008 CR and k-man have it. imran, right answer with incorrect math - translating words to equations was the real task. JarZe, probably answered who drove the car but didn't say which he specified. As they used to tell me in school ... show your work. preflop, Prime, took the road less traveled [pun intended], as always. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 3, 2008 Report Share Posted October 3, 2008 CR and k-man have it. imran, right answer with incorrect math - translating words to equations was the real task. JarZe, probably answered who drove the car but didn't say which he specified. As they used to tell me in school ... show your work. preflop, Prime, took the road less traveled [pun intended], as always. If english is not your native language then it can happen Quote Link to comment Share on other sites More sharing options...
0 Prime Posted October 3, 2008 Report Share Posted October 3, 2008 If english is not your native language then it can happen I second that. I interpreted "... as I had" in the "I would have ... as I had" clause as the actual distance traveled -- not as the distance remaining. In other words: "If I had gone 3 times as far as I had, I would have half as far to go as I had gone" Quote Link to comment Share on other sites More sharing options...
Question
bonanova
It's algebra night, me lads, Alex intoned
as he set an empty mug on his fav table
at Morty's last night. And you might want
to bring a pencil along, this one is a wee
bit complicated.
Ian was home sick, so that left Davey and
Jamie to humor Alex. Pencils are ready,
they said, shoot!
So, Alex Jr. and I took a trip the other day,
one of us on our horse, the other in our
car. After a while, I observed that if I had
gone three times as far as I had, I would
have half as far to go as I had; and if Jr.
had gone half as far as he had, he would
have three times as far to go as he had.
By the way, we started at the same time
and place, and were headed for the same
destination. Did you get all that?
They nodded, but Davey was stroking
his beard just a little more vigorously
than usual. OK, they said, but ... what's
the question?
The question, lads is this: which one of
us rode the horse?
It took Davey only a minute to answer.
I think I know...
Do you?
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