The train consists of 6 carriages, 20 meters long each. The gap between the carriages is 1 meter. If the train is moving at a constant speed of 60 km/h, how much time will it take the train to run through a 1 kilometer tunnel?

1,125 minutes

Step-by-step explanation:

The train is cross the tunnel at constant speed. Therefore, the speed is the ratio of the sum of the distance travelled and the total length of the train to the speed. That is to say:

1.125 minutes

Step-by-step explanation:

The train consists of 6 carriages each of length 20 metres

Total Length of Carriages = Number of Carriage X Length Per Carriage =20 X 6

=120 metres

Gap between the carriages= 1 metre each

There are a total of 5 gaps between the carriages = 5X 1= 5m

Therefore Total Length of the train= Total Carriage Length + Total Gap Length

= 120+5= 125 metres

Total Distance Required o Cross the Tunnel= 1km + 125 metres

= 1.125km

The Speed of the Train = 60km/hr

Time Required = Distance /Speed

= 1.125/60= 0.01875 hours

We can convert the hour to minutes by multiplying by 60

0.01875 hours = 0.01875 X 60 minute = 1.125 minutes

Therefore the train requires 1.125 minutes to cross the tunnel.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

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