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Is this solvable? (1 Viewer)

Chemical X

Chemical X

Footballguy
Giovanna is a commuter.
Every day, after work, she takes the train and arrives at the station in her town at 6.00 pm where she finds her husband Mario waiting for her with the car to return home.
Today Giovanna finished early, she arrives at the station in her town at 5pm, since it is good weather she decides to walk along the same road that Mario travels in the car so as to meet him during his journey.
When they meet, Giovanna gets into the car and arrive home 10 minutes earlier than usual.
Assuming that Mario left just in time to arrive at the station at 6:00pm, can you determine how long Giovanna walked before meeting Mario?
 
Certainly not without making some assumptions (Mario drives the same speed every day, in both directions; Mario leaves the house at precisely the same time every day, thus waiting at the station the same length of time every day).

With those assumptions, it still does not seem solveable without knowing at least the normal time they arrive home.
 
Psychopav said:
Certainly not without making some assumptions (Mario drives the same speed every day, in both directions; Mario leaves the house at precisely the same time every day, thus waiting at the station the same length of time every day).

With those assumptions, it still does not seem solveable without knowing at least the normal time they arrive home.
Click to expand...
yeah. my wife took an online italian course and the guest speaker was a mathematician. now, i’m no mathemagician, but i felt this was unsolvable unless you make assumptions.
my guess was he leaves home at 5.50p, gets to the station at 6p and they return home at 6.10p. so, she walks 55 minutes to make his back and forth trip 1/2. he gets her at 5.55p and they are home at 6p. me fail math, that’s unpossible!!
 
Don Quixote said:
55 minutes? Saved 10 minutes total — 5 minutes each way (to station from where picked up, and back from station to that spot).
Click to expand...

Exactomundo. Just think of it from the car's standpoint. The driver cut out 10 minutes of driving time, half of it from not going all the way to the station, and the other half of it from having a shorter drive back.

He would have arrived at the station at 6pm but instead met her 5 minutes earlier. So he had to meet her at 5:55 and that means she walked 55 minutes.
 
Let's say the drive to the station is 1 hour. On a normal day, he leaves at 5, gets there just in time (as is assumed) at 6, picks her up, drives back and arrives at 7pm. But on this day, she arrives at 5 and starts walking. He leaves at 5, meets her at some point in the middle, picks her up, drives back, and arrives at 6:50PM. So he saved 10 minutes.

If the drive is 30 minutes... normal day he leaves at 5:30, gets there at 6, picks her up, drives back, they arrive at 6:30. But this day they arrive at 6:20. So he saved 10 minutes from a normal day.

So her walk means she was 5 minutes closer to the house when he met her somewhere in the middle. She would have walked 55 minutes and cut 5 minutes from his journey.

Edit: yeah what y'all said
 
ghostguy123 said:
so the distance they live and the MHP of the roads dont matter?
Click to expand...

Correct, they don't matter.. They would have to live more than 5 driving minutes from the train station or else it's not a possible situation, but otherwise distance and speed limits don't matter.
 
What you're solving amounts to two questions:

1) A car normally drives to the station, arriving at 6, then turning around and driving home to arrive home at the same time each day. This time it turns around early and arrives home 10 minutes earlier than normal. What time did the car turn around? (Saved 10 minutes, half driving there, half back, so it turned around 5 minutes short of 6pm).

2) If someone starts walking at 5pm and stops at the time that is the answer from part 1, how long did they walk?
 
Runkle said:
Let's say the drive to the station is 1 hour. On a normal day, he leaves at 5, gets there just in time (as is assumed) at 6, picks her up, drives back and arrives at 7pm. But on this day, she arrives at 5 and starts walking. He leaves at 5, meets her at some point in the middle, picks her up, drives back, and arrives at 6:50PM. So he saved 10 minutes.

If the drive is 30 minutes... normal day he leaves at 5:30, gets there at 6, picks her up, drives back, they arrive at 6:30. But this day they arrive at 6:20. So he saved 10 minutes from a normal day.

So her walk means she was 5 minutes closer to the house when he met her somewhere in the middle. She would have walked 55 minutes and cut 5 minutes from his journey.

Edit: yeah what y'all said
Click to expand...
What if traffic is worse between 5:00 and 6:00 than from 6:00 to 7:00?
 
GregR said:
ghostguy123 said:
so the distance they live and the MHP of the roads dont matter?
Click to expand...

Correct, they don't matter.. They would have to live more than 5 driving minutes from the train station or else it's not a possible situation, but otherwise distance and speed limits don't matter.
Click to expand...
They would matter if the question were how fast or how far she walked rather than how much time she walked.
Otherwise, you just have to assume the same rate of travel in the car for the forward and reverse drive and that rate is consistent day to day, right?
 
GregR said:
ghostguy123 said:
so the distance they live and the MHP of the roads dont matter?
Click to expand...

Correct, they don't matter.. They would have to live more than 5 driving minutes from the train station or else it's not a possible situation, but otherwise distance and speed limits don't matter.
Click to expand...
Before I looked more deeply into trying to solve, just wanted to toss out that question so I dont spend time trying to figure out a trick question.
 
jhib said:
GregR said:
ghostguy123 said:
so the distance they live and the MHP of the roads dont matter?
Click to expand...

Correct, they don't matter.. They would have to live more than 5 driving minutes from the train station or else it's not a possible situation, but otherwise distance and speed limits don't matter.
Click to expand...
They would matter if the question were how fast or how far she walked rather than how much time she walked.
Otherwise, you just have to assume the same rate of travel in the car for the forward and reverse drive and that rate is consistent day to day, right?
Click to expand...
I believe so yes. They keep time as the only thing we have to work with. If you want to get into distance or speed we'd need more information.
 
GregR said:
What you're solving amounts to two questions:

1) A car normally drives to the station, arriving at 6, then turning around and driving home to arrive home at the same time each day. This time it turns around early and arrives home 10 minutes earlier than normal. What time did the car turn around? (Saved 10 minutes, half driving there, half back, so it turned around 5 minutes short of 6pm).

2) If someone starts walking at 5pm and stops at the time that is the answer from part 1, how long did they walk?
Click to expand...
This makes sense. Thanks!
 
No. Traffic. What shoes Giovanna is wearing. What did Giovanna eat for lunch. Would that make her walk slower. Is it raining. Too many variables. Case closed, Murdock.
 
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