Brain Teasers
Race Against Time
A child in the remote mountain village of Pliluk has fallen ill. Dotan, his brother Forak, and his sister Loti must get their father, the village healer, who is gathering herbs on the other side of the mountain. To make sure they get him as quickly as possible, they decide to split up. Forak will ride his horse around the mountain's base, Dotan will travel by river raft, and Loti will climb the steep cliff trail.
The raft can travel at 22 miles an hour along the 40 miles of the river, but there are 3 places where Dotan, at each place, will lose 0.4 hours by having to carry the raft around dangerous waterfalls. Forak's horse can travel 15 miles per hour on the flatter part of the 32-mile trail, but only 8 miles per hour on the steep part, which is 30% of the whole trail. Loti's road up and down the cliffs is the shortest, only 14 miles, but her average rate is only 5 miles an hour, and she must take a 10-minute rest at the summit.
Assuming Dotan does not hit a rock, Forak is not attacked by an ice panther, and Loti is not bitten by a cliff snake, who will reach their father first? Round all decimals to tenths.
The raft can travel at 22 miles an hour along the 40 miles of the river, but there are 3 places where Dotan, at each place, will lose 0.4 hours by having to carry the raft around dangerous waterfalls. Forak's horse can travel 15 miles per hour on the flatter part of the 32-mile trail, but only 8 miles per hour on the steep part, which is 30% of the whole trail. Loti's road up and down the cliffs is the shortest, only 14 miles, but her average rate is only 5 miles an hour, and she must take a 10-minute rest at the summit.
Assuming Dotan does not hit a rock, Forak is not attacked by an ice panther, and Loti is not bitten by a cliff snake, who will reach their father first? Round all decimals to tenths.
Hint
Choose your mathematical operations carefully.Answer
Forak will reach his father first.At the rate of 22 miles per hour, Dotan's raft covers the distance of 40 miles in 40/22 = 1.8 hours. Adding the time for three delays, 3*0.4 = 1.2 hours, his total time is 3 hours.
Thirty percent of Forak's 32-mile trail (or 32*0.3 = 9.6 miles) is steep, and at a rate of 8 miles per hour he covers this steep section in 9.6/8 = 1.2 hours. At a rate of 15 miles per hour on the 22.4-mile flat section, Forak covers this in 22.4/15 = 1.5 hours. His total time is 2.7 hours.
At her average rate of 5 miles per hour, Loti covers her 14-mile mountain trail in 14/5 = 2.8 hours, but her rest time at the summit takes 10/60 or nearly 0.2 hours, so her total time, like Dotan's, is 3 hours.
Their father rides Forak's horse back to the village and treats the child. The child recovers, to everyone's joy.
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Great job, Faire!
I'm going to throw something out there that is NOT specified as a condition in the teaser. The math is perfect for the teaser as shown. However, the father would NOT want to take the horse back to the village (as stated in the teaser) if he wanted to get back in the fastest amount of time. Why is this?
(This assumes that all stated time and distance measurements remain the same and apply to the father also; i.e. the horse doesn't go slower because there are now two people on it's back.)
I'm going to throw something out there that is NOT specified as a condition in the teaser. The math is perfect for the teaser as shown. However, the father would NOT want to take the horse back to the village (as stated in the teaser) if he wanted to get back in the fastest amount of time. Why is this?
(This assumes that all stated time and distance measurements remain the same and apply to the father also; i.e. the horse doesn't go slower because there are now two people on it's back.)
He would not want to take the horse back to the camp because he would, by virtue of the description of the trail, never arrive back at the camp. How can a round trip horse trail be either flat or steep (inclined) and ever allow the rider to arrive back at the same place (altitude) from where he began? It's impossible!
Hmm, not exactly what I was thinking but you're on the right track (ok, pun intended hehe).
To AwwwSweet's tease- Forak's horse is tired. When it was fresh, it slowed to 8 mph on inclines that must have been mostly downhill. How can it help but climb those same slopes uphill at a much slower pace? The speed of the raft proves the father is downstream and, hence, at a lower altitude. It also means that even if the father saved a few minutes by riding the tired horse upstream to meet Dotan, it would be foolish to consider a return trip going against such a strong current.
Father, with his experience and maturity, will probably climb the cliff trail and do so faster than Loti.
Father, with his experience and maturity, will probably climb the cliff trail and do so faster than Loti.
The problem was simple to solve but the comments are thought provoking!
Stil - Basically, yes, but not even taking into account that the horse is tired. Now I admit I am assuming a bit, but the speed of the raft does suggest that the father is at a lower altitude. (Logically, it would be impossible for one person to paddle 22 miles in an hour, especially against a current.) The father would obviously not wait for the raft, which would be out of the question anyway.
As such, if the horse has to climb (or even descend?) steep areas to get to a lower altitude, then it is reasonable to assume that the return path would indeed be slower. For simplicity (though it could be explained further), assume the horse returns at 10mph the entire route, totaling 3 hours, 12 minutes. If the father only traveled at the same pace as Loti through the cliffs, with the 10 minute break, he would still return back at the village in 2 hours, 58 minutes.
That is of course assuming that the father is also not bitten by a cliff snake.
As such, if the horse has to climb (or even descend?) steep areas to get to a lower altitude, then it is reasonable to assume that the return path would indeed be slower. For simplicity (though it could be explained further), assume the horse returns at 10mph the entire route, totaling 3 hours, 12 minutes. If the father only traveled at the same pace as Loti through the cliffs, with the 10 minute break, he would still return back at the village in 2 hours, 58 minutes.
That is of course assuming that the father is also not bitten by a cliff snake.
u speak me language
You can't say "round to the nearest tenth" for this. Each second count!
Putting into the account the given weird conditions, Loti will arrive exactly 1 minute and 36 seconds ahead of Forak.
Loti = 2.666666667 hrs
Forak = 2.693333333 hrs
Dotan = 3.018181818 hrs
Putting into the account the given weird conditions, Loti will arrive exactly 1 minute and 36 seconds ahead of Forak.
Loti = 2.666666667 hrs
Forak = 2.693333333 hrs
Dotan = 3.018181818 hrs
The comments are better than the "teaser" which is really just a glorified math problem with no tease.
To everyone suggesting that the father would return on foot in the same time as Loti took to travel there, consider that
A) the route to the father was overall downhill while the route back is overall uphill;
B) the father must have walked to get there and has been search for herbs, so he is not necessarily fresh; and
C) Loti is younger than her father and thus perhaps faster.
I think taking the horse back makes perfect sense, but Forak should walk back so as not to slow the horse down.
To everyone suggesting that the father would return on foot in the same time as Loti took to travel there, consider that
A) the route to the father was overall downhill while the route back is overall uphill;
B) the father must have walked to get there and has been search for herbs, so he is not necessarily fresh; and
C) Loti is younger than her father and thus perhaps faster.
I think taking the horse back makes perfect sense, but Forak should walk back so as not to slow the horse down.
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