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# help

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A train leaves Canberra for Sydney at 12 noon and another train leaves Sydney for Canberra forty minutes later. Both travel at the same constant speed, taking 3 1/2 hours to complete the journey. At what time will they pass?

May 4, 2020

#1
+651
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The two trains meet after 125 minutes the first starts or at 2:05 pm

May 4, 2020
#2
+111430
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The distance between the towns  must  be  (3.5) S =  (7/2)S  where  S is the speed that each person travels

And 40 min  = 2/3  hr

Call  T  the time (in hrs)  it  takes  for the first person to travel to meet the second

But  the second person  has   traveled  40 mintues less =  [ T - (2/3)] hrs  when they meet

So...we  have this equation

Distance  traveled by first person +  Distance traveled by second person  = total distance  between towns

So  we  have

S (T)  + S [ T - 2/3]   = (7/2)S       divide through by S

T  + T   - 2/3  =  7/2

2T  - 2/3  =    7/2       Multiply through by 6

12T  - 4  = 21       add 4 to both sides

12T  = 25        divide both sides by  12

T  =  25/12  hrs  =   2 + 1/12  hrs  =   2 hr 5 min

They  will pass at   [ 12  + 2 hr 5 min ] =      2:05  PM

May 4, 2020
edited by CPhill  May 4, 2020
edited by CPhill  May 4, 2020