Please help me on a very hard Algebra question!?
The addams’ family was planning a fall hike to see their relatives. They were only 20 min. from the cemetery party when night quickly fell and they needed to light their one lantern to see the way. upon lighting the lantern, they realized that they were on the edge of an old bridge over a deep gully. Mortica read the sign next to the bridge, “Warning: only 2 people on this narrow, shaky old bridge at a time… the trolls are watching” having crossed other bridges before, Mortica knew that it would take her 10 min. to cross the bridge, whereas, it only took gomez only 8 min. Cousin itt who could cross in 3 min. and thing in 1 min.
When any two people cross the bridge, their speed is equal to that of the slower one. of course, for safety purposes, the lantern must be used while crossing the bridge.
My teacher said that there is a solution to this problem.. i just can’t seem to find one
Logan is technically right that you did not ask a question. I’m going to assume that you want the family to get across the bridge in 20 min, though.
There will always be at least 10 min spent crossing the bridge, since Morticia must cross at some point, and she can never “hide” her time behind a slower person, because there isn’t one.
When Morticia crosses, there are two options:
1) Gomez does not cross with her
Then there will be an additional 8 minutes minimum added to the time, because Gomez must cross at some point, and there will be no one with a higher time to cover him. Morticia can never cross back or we’ll hit the 20 minute mark immediately.
So there would be a minimum of 18 min. But, when Gomez does cross, someone must have come across the bridge to bring the lantern to him. If he’s the first to cross, Thing must be the one to go with him. Either way, it can only be Thing, otherwise we’d have 18 + 3 = 21 min at a minimum. So, there would actually be a minimum of 19 min. If Thing returned for Gomez, though, Itt cannot have been on the other side. If he were, Thing must have gone across with at least Morticia or Itt, so at least 3 more min would be incurred, bringing the total to 22. Otherwise, Itt would have to cross after Thing returns from crossing with Gomez, which would be another 3 + 1 = 4 min for a total of 23 min.
So Gomez must cross with Morticia.
2) Gomez does cross with her.
Then someone must return with the lantern. If they cross first, Gomez must return the lantern. He must eventually cross back again, costing another 8 minutes as explained in option 1), so this is impossible. So Itt and Thing must cross first. This leads to two sub-options:
Itt and Thing cross with lantern – 3 min – Total: 3 min
Thing returns with the lantern – 1 min – Total: 4 min
Morticia/Gomez cross with lantern – 10 min – Total: 14 min
Itt returns with the lantern – 3 min – Total: 17 min
Itt and Thing cross again with lantern – 3 min – Total: 20 min
OR
Itt and Thing cross with the lantern – 3 min – Total: 3 min
Itt returns with the lantern – 3 min – Total: 6 min
Morticia/Gomez cross with lantern – 10 min – Total: 16 min
Thing returns with the lantern – 1 min – Total: 17 min
Itt and Thing cross again with lantern – 3 min – Total: 20 min
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