SOLUTION: Alice and Bob started to walk towards each other’s home and then back to theirs, with steady speeds. Alice passed by a bus station at 25 m away from her home, while at the same tim

Algebra.Com
Question 1120244: Alice and Bob started to walk towards each other’s home and then back to theirs, with steady speeds. Alice passed by a bus station at 25 m away from her home, while at the same time Bob was passing by an abandoned old car. Afterwards, they met at 55 m away from Bob’s home and then they met again at 85 m from Alice’s home. What is the distance between the bus station and the abandoned car?
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Let  S  be the distance between their homes, in meters.

Let    be Alice's rate, and   be Bob's rate.

Let    be the time after their start to their first meeting.

Let    be the time after their start to their second meeting.


     Notice I follow your  (your ?)  designations in your  (your ?)  set up in

          https://math.stackexchange.com/questions/2859310/distances-and-speeds

          https://math.stackexchange.com/questions/2859310/distances-and-speeds


Then you have 

     = S - 55;      = 55;           (1)

     = 2S - 85;      = S + 85.      (2)


From (1) you have   = ;               (3)

From (2) you have   = ,              (4)

which gives you an equation for S


     = .


Simplify and solve for S:

    (S-55)*(S+85) = (2S-85)*55

    S^2 -55*S + 85*S - 55*85 = 110*S - 55*85

    S^2 - 55*S + 85*S - 110*S = 0

    S^2 - 80*S = 0

    S*(S-80) = 0  ====>  The only positive root is   S = 80.


Thus we found the distance between the homes: it is 80 meters.


Having this known,  you van calculate the ratio of their rates from (3)

     =  =  =    

and hence calculate the distance "x" from the Bob's home to the abandoned car from the proportion

     =   ======>  x =  = 55 m.


Then the distance under the question is  80 - 25 - 55 meters = 0 meters.


RELATED QUESTIONS

Alice borrowed a bicycle from her friend, Bob, and wanted to return it. She rode the... (answered by ankor@dixie-net.com)
5) Alice is trying to send a message to Bob. Eve is an eavesdropper who randomly corrupts (answered by mathmate)
Alice and Bob each have a certain amount of money. If Alice receives dollars from Bob,... (answered by ankor@dixie-net.com)
Alice and Corinne stand back-to-back. They each take 10 steps in opposite directions away (answered by edjones)
Alice and Corinne stand back-to-back. They each take 10 steps in opposite directions away (answered by CubeyThePenguin)
Alice and Corinne stand back-to-back. They each take 10 steps in opposite directions away (answered by CubeyThePenguin)
Alice and Bob play three chess games. Alice is 10 times more likely to win a game than... (answered by ikleyn,greenestamps)
Alice, Ben, and Carl collect stamps. They exchange stamps among themselves according to... (answered by ikleyn)
Alice, Bob, and Cindy each drive about1000 miles per month. Alice drives a truck which... (answered by ikleyn)