Question

6. If you start with 200 MNM's and eat 15 every minute and your friend starts with300 MnM's but eats 25 every minute. When will you have the same number asyour friend? How much longer will it take you to finish your MnM's? At 10minutes you both will have 50 left. You will finish 1 min and 20 seconds after yourfriend.

Answer 1

Given:

The initial number of MNMs I have, x=200.

The number of MNM's eat by me every minute, p=15.

The initial number of MNMs my friend have, y=300.

The number of MNM's eat by friend every minute, q=25.

Let n be the number of minutes after which both will have the same number of MNM. Then, the amount of MNM remaining with me after n minutes is,

`x-pn`

The amount of MNM remaining with my friend after n minutes is,

`y-qn`

Equate the above expressions and substitute the values to find the number of minutes n.

`\begin{gathered} x-pn=y-qn \\ 200-15n=300-25n \\ 25n-15n=300-200 \\ 10n=100 \\ n=(100)/(10) \\ n=10 \end{gathered}`

Therefore, I will have the same number as my friend after 10 minutes.

The number of minutes taken by me to finish 200 MNM's is,

`\begin{gathered} m=(x)/(p) \\ =(200)/(15) \\ =13(5)/(15) \\ =13(1)/(3)\text{minutes} \\ =13\text{minute}+(1)/(3)\min utes*\frac{60\text{ seconds}}{1\text{ minute}} \\ =13\text{ minutes +20 seconds} \end{gathered}`

So, I will take 13 minutes 20 seconds to finish the MNM's.

The number of minutes taken by my friend to finish 300 MNM's is,

`\begin{gathered} k=(y)/(q) \\ =(300)/(25) \\ =12\text{ minutes} \end{gathered}`

So, the friend will take 12 minutes to finish the MNM's.

So, I will finish