Question

at a football stadium it takes one hour for the spectators to get in if 6 gates are used. how long will it take them to get in if 3more gates are opened?​

Answer 1

If it takes one hour for the spectators to get in using 6 gates, we can calculate the rate of spectators entering per gate per hour. Let's denote this rate as
`\displaystyle\sf R`.

So,
`\displaystyle\sf R = \frac{{\text{{Number of spectators}}}}{{\text{{Time taken}}}} = \frac{{\text{{Number of spectators}}}}{{1 \text{{ hour}}}}`.

Now, if we open 3 more gates, the total number of gates becomes 6 + 3 = 9 gates.

Since the rate of spectators entering per gate per hour remains the same, the total rate of spectators entering per hour will be
`\displaystyle\sf 9R`.

To find the time it will take for spectators to get in using 9 gates, we need to divide the total number of spectators by the rate.

Let's denote the time taken to get in using 9 gates as
`\displaystyle\sf T`.

So,
`\displaystyle\sf T = \frac{{\text{{Number of spectators}}}}{{9R}} = \frac{{\text{{Number of spectators}}}}{{9 * \left( \frac{{\text{{Number of spectators}}}}{{1 \text{{ hour}}}} \right)}} = \frac{{1}}{{9}} \text{{ hour}}`.

Therefore, it will take
`\displaystyle\sf \frac{{1}}{{9}}` hour for the spectators to get in if 3 more gates are opened, which is approximately 6.67 minutes.