Lesson One very twisted Travel and Distance problem

One very twisted Travel and Distance problem

Problem 1

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.


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 =  = 44 m.


Then the distance under the question is  80 - 20 - 44 meters = 16 meters.