Question

On a ring road, 12 trams are spaced at regular intervals and travel at a constant speed. How many trams need to be added to the circuit so that, maintaining the same speed, the intervals between them will decrease by 1 5

Answer 1

3 trams must be added

Explanation:

In this problem, there are 12 trams along the ring road, spaced at regular intervals.

Calling L the length of the ring road, this means that the space between two consecutive trams is

$d=\frac{L}{12}$ (1)

In this problem, we want to add n trams such that the interval between the trams will decrease by 1/5; therefore the distance will become

$d'=(1-\frac{1}{5})d=\frac{4}{5}d$

And the number of trams will become

$12+n$

So eq.(1) will become

$\frac{4}{5}d=\frac{L}{n+12}$ (2)

And substituting eq.(1) into eq.(2), we find:

$\frac{4}{5}(\frac{L}{12})=\frac{L}{n+12}\\\rightarrow n+12=15\\\rightarrow n = 3$

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Answer 2

Answer: 3

Explanation:

We need to do (1/(5-1))x12