Question

Snuggles, a toy company's train, is 1000 metres long. It is travelling at a uniform speed, and a 3000m tunnels awaits. Thirty seconds pass from the time the last car has just completely entered the tunnel until the time when the front of the engine emerges from the other end. Determine the speed of the Snuggles, in km/h.

Answer 1

The speed of the Snuggles is 480 kilometers per hour.

Explanation:

The speed of the train (
`v`), in meters per second, is the sum of the length of the tunnel (
`L`), in meters, plus the length of the train (
`l`), in meters, divided by time taken by vehicle to cross the tunnel completely (
`t`), in seconds:

`v = (l+L)/(t)` (1)

If we know that
`l = 1000\,m`,
`L = 3000\,m` and
`t = 30\,s`, then the speed of the train is:

`v = (l+L)/(t)`

`v = (1000\,m + 3000\,m)/(30\,s)`

`v = 133.333\,(m)/(s)`

A kilometer per hour equals 3.6 meters per second. By unit conversion, we conclude that speed of the train is:

`v = 479.998\,(km)/(h)`

The speed of the Snuggles is 480 kilometers per hour.