Question

Please answer all questions. Please show your work in the answers.I skated 3 miles in 5 minutes.a. How many miles per minute is that?b. I skated 3 miles in 5 minutes. How many minutes per mile is that?c. If I skated 3 miles in 5 minutes, how far will I skate in an hour?ML and MC live 37 miles apart from each other. ML drives at a speed of 8 miles per hour, and MC drives at a speed of 4 miles per hour. How long does it take until ML and MC meet?Protein bar A has 15 grams of protein in a 40 gram bar. Protein bar B has 20 grams of protein in a 60 gram bar. Which bar has more protein per gram?

Answer 1

1)

a) In order to find the value of miles per minute, we just need to divide the number of miles by the number of minutes:

`\frac{3\text{ miles}}{5\text{ minutes}}=(3)/(5)\text{ miles/minute}`

So the result is 3/5 miles per minute.

b) In order to find the number of minutes per mile, since we have the value of miles per minutes, we just need to invert the fraction:

`\frac{3\text{ miles}}{5\text{ minutes}}=\frac{5\text{ minutes}}{3\text{ miles}}=(5)/(3)\text{ minutes/mile}`

So the result is 5/3 minutes per mile

c)

In order to calculate the distance after 1 hour (60 minutes), we can use a rule of three:

`\begin{gathered} 5\text{ minutes}\to3\text{ miles} \\ 60\text{ minutes }\to x \\ \\ (5)/(60)=(3)/(x) \\ (1)/(12)=(3)/(x) \\ x=3\cdot12=36\text{ miles} \end{gathered}`

So the result is 36 miles.

2)

Since they are going towards each other, the relative speed is the sum of their speeds:

`V=8+4=12\text{ mph}`

Now, to find the time, we just need to divide the distance by the speed:

`t=(37)/(12)=3.083=3\text{ hours 5 minutes}`

So the amount of time is 3 hours and 5 minutes.

3)

In order to find which bar has more protein, let's compare the fractions that represents the amount of protein in each bar:

`\begin{gathered} \text{bar A: 15/40 of protein} \\ \text{bar B: 20/60 of protein} \\ \\ (15)/(40)=(45)/(120) \\ (20)/(60)=(40)/(120) \\ (45)/(120)>(40)/(120) \end{gathered}`

So protein bar A has more protein per gram.