Question

I tried by Listing Method below because of the looping effect going round and round unlike straight lines.

Fastest car travelled at 180km/h. For each  complete round is 36km, time taken is 36/180 x 60min = 12 min. Every 12 min, fastest car completes 1 round, and its distance from start line resets to 0km-mark.

Every 12min, slowest car travelled 100 x 12/60 =20km

Fast car at   Slow car travelled      Fast car pass

12min             20km, 0) 20km-mark     0 time

24min            40km, 1) 4km-mark        0 time

36min            60km, 1) 24km-mark      1 time

48min           80km, 2) 8km-mark        Still 1 time

60min          100km 2) 28km-mark      2 times

72min           120km  3) 12km-mark     Still 2 times

84min          140km  3) 32km-mark      3 times

60min x 32 to catch up/(180-100) = 24 more min to overtake to pass 4th time.

108min     100×108/60 = 180km, 0km-mark   4th time exact

3pm … add 108min  —> 4:48pm# (pls counter check solution & given method)

[or add on 12 mins in table]

96min         160km   4) 16km-mark     Still 3 times

108min       180km  5) 0km-mark       Exact 4th time

Method 2:

After first 12 mins, slowest car is 20 km “ahead” of fastest car. The fastest car will take 60x 20/(180-100) = 15 mins to catch up 1st time. So 12+15=27 mins to catch up once for both cars to be at the same exact spot on the loop.

So to catch up 4th time –> 27×4 = 108 mins , or 4:48pm#

Method 2 and 3 only came to me because I got the solution and visualising by Listing Method, so can comfortably agree with the logic and accuracy.

Method 3 :

Fast Car :  Slow Car : Difference

Speed                                        180   :    100      :

Ratio of speed                           9     :     5           :   4

Ratio of distance                      9      :     5          :    4

Actual distance 1st pass          81    :     45        :   36km (Fastest car has completed 1 more round after analysis)

Actual distance 4th pass       324   :     180      :  36 x4

Time taken = D/S =  324/180  or   180/100  = 1.8hrs = 1h 48 min

Time at 4th pass is 4:48pm#

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