A maths problem! need help ^^?

Question

A queue of people is entering a mueseum at a steady rate of 10 people every 5 minutes, which shortens the queue by 10 metres every 15m minutes. when the meuseum opens, there are 90 people in the queue. No one else joins the queue until Frank and his 5 friends join the queue, 12 minutes after the meuseum opens. Including Frank and his friend, how long is the queue at that point in time?

Thanks ^^

Answer 1

The problem can be analysed thus:
If there are 10 people entering the museum every 5 minutes, that means there can be 2 people entering every minute.

If the queue shortens by 10 metres every 15 minutes, that means 10 metres is the length of a queue of 30 people (15 minutes X 2 people per minute). This in turn means that a single person occupies 1/3 metre space in the queue.

Since 12 minutes have passed, 24 people (12 minutes X 2 people per minute) out of the original 90 have entered the museum. This leaves 66 people outside. Now, Frank and his 5 friends (6 people in all) join the queue. The queue now contains 72 people.

At 1/3 metre per person, the length of the queue now is:
24 metres, that is 72 X 1/3 metre.

Answer 2

If 10 people enter the museum in 5 minutes, 2 people are entering every minute (10 divided by 5).

Hence in 12 minutes of opening, 12 x 2 i.e. 24 people have entered and 90 minus 24 i.e. 66 people are still in the queue, when Frank joins the queue. So he is the 67th person in the queue and after him are his 5 friends. So there are totally 67+5= 72 persons in the queue at that point in time.

The 66 persons before Frank will enter the museum in 33 minutes (66 divivded by 2) and Frank will enter in the 34th minute of standing in the queue.

Next,
Every 15 minutes, the queue shortens by 10 metres.
In 15 minutes, 30 persons enter at the given rate
i.e. 10 metres reduced by 30 persons entry
hence 1/3 metre reduced by 1 persons entrySince 72 persons are in the line when Frank joins in with his 5 friends, it will be 1/3 multiplied by 72 = 24 metres long

Answer 3

10 x 5 = 50
10 metres= 30 peaople couz 15 minute
90 #

Not at my level!!!