Race Against TimeMath brain teasers require computations to solve.
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.
HintChoose your mathematical operations carefully.
AnswerForak 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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