Brain Teasers
Mad Ade's Bus Journey
Mad Ade goes to work, testing Kebabs at the local "Sweaty Chef Kebab shop", by bus. One day he falls asleep when the bus still has twice as far to go as it has already gone.
Halfway through the trip he wakes up as the bus bounces over some bad potholes. When he finally falls asleep again, the bus still has half the distance to go that it has already traveled. Fortunately, Mad Ade wakes up at the end of his trip.
What portion of the total trip did Mad Ade sleep?
Halfway through the trip he wakes up as the bus bounces over some bad potholes. When he finally falls asleep again, the bus still has half the distance to go that it has already traveled. Fortunately, Mad Ade wakes up at the end of his trip.
What portion of the total trip did Mad Ade sleep?
Answer
Mad Ade is asleep for a total of 1/2 of the trip.You can divide the trip into 6 equal parts.
Mad Ade falls asleep 2/6 (1/3) of the way through the trip. He awakes at 3/6 of the way through the trip. So far, he has slept 1/6 of the way.
He falls asleep again at 4/6 (or 2/3) of the way through the trip and sleeps until he gets off. He therefore sleeps 2/6 more.
1/6 plus 2/6 equals 3/6 or 1/2.
If you wanted to use numbers as an example. Say the trip is 90 miles long.
90 X 2/6= 30 He has twice as far to travel as he already has so at this point he would still have to travel 60 miles.
1/2 way through the trip is 90 X 3/6=45.
So far he has slept for 15 miles.
He falls asleep again when he still has half the distance left that he already has traveled. 90 X 4/6 =60 miles (traveled so far). Half of 60 is 30 miles. So he has 30 miles left to travel and he is asleep during this time. 30 + 15=45 which is half of 90.
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Comments
Nice Mathematical word puzzle. I like the use of "half as far..." and "twice as far..." to get the thirds.
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