Quadratic equations early train word problem

[Prakriti]

Hello everyone. My son is in grade 10. He takes the IB math course. He is struggling with a really difficult quadratic word problem. I can usually help him with solving for roots, finding vertex etc but I am out if my depth here. Please help us. Thank you!

"Karen catches an earlier train than planned and arrives at her home station 36 minutes before her father is due to meet her on the later train. She promptly sets out to jog home at 7.5 km/hr knowing she will meet her father coming for her. They meet when he has driven 32 km from home. She arrives 8 minutes earlier than if she had caught the later train. How far is Karen's home from the station. What was the average speed of the car? "

It's a speed distance time question so I figure I should solve for distance first in terms of speed and time. I don't know how to set up the equation. Please help.

 

[stapel]

Hello everyone. My son is in grade 10. He takes the IB math course. He is struggling with a really difficult quadratic word problem.

We have learned, from hard experience, that attempting to work through a "translator" who doesn't "speak the language" is not likely to end well. We really do need to speak with the actual student.

"Karen catches an earlier train than planned and arrives at her home station 36 minutes before her father is due to meet her on the later train. She promptly sets out to jog home at 7.5 km/hr knowing she will meet her father coming for her. They meet when he has driven 32 km from home. She arrives 8 minutes earlier than if she had caught the later train. How far is Karen's home from the station. What was the average speed of the car? "

Please have you son reply with his thoughts and efforts so far, so we can see where he's having trouble. Thank you!

 

[Prakriti]

Thank you for taking the time to add your thoughts. As the mother of a young teenager, I reserve the rights to restrict my son's access to the Internet. You do not have to agree with my decision. You also do not need to help me if my information is not sufficient enough. As far as I am aware, I have provided all the information I had. I have also mentioned precisely where he is facing difficulty. Also, I have already gone through a few earlier posts in this forum itself where parents have asked questions on behalf of their children. I'm hopeful someone will help be able to help me with the solution. If not, I will look elsewhere. And if it is the general consensus of the forum (including moderators) that only students should be posting questions, I suppose this would have been mentioned as a disclaimer somewhere. Once again, thank you for your help.

 

[Deleted member 4993]

Hint:
twice the distance (to and fro) jogged by Karen will
not need to be driven by father: this is what causes
the time reduction of 8 minutes.

Suggestion:
make up an easy case, like 100 miles from home to
station, father travelling @ 20 kph, Karen jogging @ 5 kph.
Then you'll be able to "see" what d'heck is going on

That would complicate things.....

 

[Steven G]

Huh? kmph?

There you go confusing yourself again.

 

[Deleted member 4993]

OK OK I get it: I used miles and kms in same problem
1st mistake this year...

No .... third mistake!!

What is that? kilometers/second ? kilometers * second?

To the corner ... double time.....