Zuleica's mother Wilma picks her up at the train station when she comes home from school, then Wilma drives Zuleica home. They always return home at 5:00 p.m. One day Zuleica left school early and got to the train station an hour early. She then started walking home. Wilma left home at the usual time to pick Zuleica up, and they met along the route between the train station and their house. Wilma picked Zuleica up and then drove home, arriving at 4:48 p.m. For how many minutes had Zuleica been walking before Wilma picked her up?

 Jul 10, 2019

she has been walking 22 min

 Jul 10, 2019

For this problem....I'm assuming that the mother and daughter normally arrive at the train station at the same time

I'm also assuming that "between the station and their house" means halfway between the station and the house


Call the distance from the house to the train station , D

So....the distance that the mother would normally drive is 2D

And let her rate be   R

And let the time that she would normally drive be = T   (in hours)

So  we have that

2D / R   = T      (1)


But..on this day.....the mother only drives  (1/2)D + (1/2)D   = D

And....if she normaly returns at 5PM, but now only returns at 4:48PM....then her normal driving time must be 12 minutes less than normal  = 1/5  hr

So.....we have that

D / R  =  T - 1/5    multiply through by 2

2D / R  = 2(T - 1/5)      (2)


This implies that   (1)  = (2)...so....

T = 2(T - 1/5)

T = 2T - 2/5

2T - T  = 2/5

T  = 2/5.......this means that her normal round-trip driving time  is 2/5 hr  =  24 min


So....she must normally leave her house at   4:36 PM   (since 24 minutes after this = 5PM)

And she would normally reach the station at 12 minutes after 4:36 PM =  4:48 PM

But....this means that she reaches the halfway point at  6 mnutes after 4:36 PM  = 4:42 PM


Now.....let's look at this from the daughter's point of view..... she would normally meet her mother at the station at  4:48 PM.....but.....since she gets there an hour early......she must reach the station at 3:48 PM  and she immediately begins walking


So.....she walks from  3:48 PM   and meets her mother at the halfway point at  4:42 PM


So....she walks for 54 min



cool cool cool

 Jul 11, 2019

It is not exactly the same problem, but the solution would be the same as this one. There are half a dozen different solutions, many of them very clever:



 Jul 11, 2019

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