Epic Systems Interview Question
Software Engineer / DevelopersCountry: United States
Interview Type: Written Test
Let the movement of person A in time t be described by A(t)
Let the movement of person B in time t be described by B(t)
Deduce A(t) and B(t) from problem statement:
A(t) = 5*t + 1
B(t) = -10*t + 106
Because at time t=0
Person A is at building 1, so A(0) = 1
Person B is at building 106, so B(0) = 106
By inspection Person A must be traversing in increasing building number, and Person B in decreasing building number, hence the sign in the equations.
When the 2 persons meet, A(t) = B(t)
Or:
5t + 1 = -10t + 106
15t = 105
t = 7
So at t=7 min they 2 people meet, and the location is given by
A(t=7) = B(t=7) = 5*7 + 1 = 36
At 36th building @ 8th minute.
Time A @ B @
1 1 106
2 6 96
3 11 86
4 16 76
5 21 66
6 26 56
7 31 46
8 36 36
The question mentioned "Person A is in building 1 and person B is in building 106" . I suppose this is the state at minute-0 and time starts from here. So, they will meet when 7 minutes would've just completely passed.
Time A @ B @
0 1 106
1 6 96
2 11 86
3 16 76
4 21 66
5 26 56
6 31 46
7 36 36
Assuming A and B are going towards each other,
at time t, A is at 1+5t, B is at 106-10t
They meet when 1+5t = 106-10t,
which is at t=7
Replace t in the equations, that's building 36.
there are 106-1 = 105 buildings distance from A to B or B to A.
when both meet, their total distance must equal 105. Hence we have this equation:
5P + 10P = 105
<=> P = 105/15 = 7
A passes 35 buildings,
B passes 70 buildings,
they met at building number 36.
At start : A-------------------------------B
when meet: ----------AB--------------------
Let buildings covered by A when they meet = x
Then buildings covered by B when they meet = 105 -x
Both of them will meet each each other exactly after travelling the same time T.
we have Speeds of A and B as,
Sa = 5 building/minute
Sb = 10 building/minute
Time = Distance x Speed, as the time taken is same we could equate Ta and Tb
Ta = Tb
x/5 = (105 - x)/10;
x = 35;
So they meet at 36th building.
Based on this statement
"The buildings of an office are numbered sequentially. Person A is in building 1 and person B is in building 106. If A crosses 5 offices in a minute and B crosses 10 offices in a minute, at which office number will they both meet?"
I don't know what number the offices are to give a proper answer, as far as what building they would meet at could be answered however but not asked for in this question.
Distance between two building is 106-1 = 105.
- Rakesh Roy April 26, 2014Relative Speed (two people moving towards each other) = 10+5 = 15.
Time taken = 105/15 = 7
At the end of seventh minute A would have travelled 7*5 = 35 building. Initially A was in building 1, so they meet at #36.