Answer :
Sure! Let's solve the given word problems step by step.
### Problem 1:
#### a. If Mohamed's soccer team can eat 6 pizzas in 30 minutes, how many pizzas would they eat in an hour?
1. First, let's find the rate at which the team eats pizzas per minute.
[tex]\[
\text{Rate} = \frac{6 \text{ pizzas}}{30 \text{ minutes}} = 0.2 \text{ pizzas per minute}
\][/tex]
2. Next, we need to find out how many pizzas they would eat in 60 minutes (which is an hour).
[tex]\[
\text{Pizzas in an hour} = 0.2 \text{ pizzas per minute} \times 60 \text{ minutes} = 12 \text{ pizzas}
\][/tex]
So, Mohamed's soccer team would eat 12 pizzas in an hour.
#### b. If Meri has 10 penalties in 4 games, what is the average number of penalties she gets in each game?
1. We need to find the average number of penalties per game.
[tex]\[
\text{Average penalties per game} = \frac{10 \text{ penalties}}{4 \text{ games}} = 2.5 \text{ penalties per game}
\][/tex]
So, Meri gets an average of 2.5 penalties per game.
### Problem 2:
#### a. On a hike Deshawn walked 28 km in 7 hours. How long will it take him to walk 100 km?
1. First, let's find Deshawn's walking rate (km per hour).
[tex]\[
\text{Rate} = \frac{28 \text{ km}}{7 \text{ hours}} = 4 \text{ km per hour}
\][/tex]
2. Next, we need to determine how long it will take him to walk 100 km.
[tex]\[
\text{Time to walk 100 km} = \frac{100 \text{ km}}{4 \text{ km per hour}} = 25 \text{ hours}
\][/tex]
So, it will take Deshawn 25 hours to walk 100 km.
#### b. A grey whale's heart beats 24 times in 3 minutes. At this rate, how many times does it beat in one day?
1. First, let's find the whale's heart rate per minute.
[tex]\[
\text{Heart rate per minute} = \frac{24 \text{ beats}}{3 \text{ minutes}} = 8 \text{ beats per minute}
\][/tex]
2. Now, we need to calculate the number of times the heart beats in one day (24 hours).
1 day = 24 hours = 24 \times 60 = 1440 minutes
[tex]\[
\text{Heart beats in one day} = 8 \text{ beats per minute} \times 1440 \text{ minutes} = 11520 \text{ beats}
\][/tex]
So, the grey whale's heart beats 11520 times in one day.
All the results have been obtained step-by-step to ensure understanding of how to solve these types of problems using unit rates and proportions.
### Problem 1:
#### a. If Mohamed's soccer team can eat 6 pizzas in 30 minutes, how many pizzas would they eat in an hour?
1. First, let's find the rate at which the team eats pizzas per minute.
[tex]\[
\text{Rate} = \frac{6 \text{ pizzas}}{30 \text{ minutes}} = 0.2 \text{ pizzas per minute}
\][/tex]
2. Next, we need to find out how many pizzas they would eat in 60 minutes (which is an hour).
[tex]\[
\text{Pizzas in an hour} = 0.2 \text{ pizzas per minute} \times 60 \text{ minutes} = 12 \text{ pizzas}
\][/tex]
So, Mohamed's soccer team would eat 12 pizzas in an hour.
#### b. If Meri has 10 penalties in 4 games, what is the average number of penalties she gets in each game?
1. We need to find the average number of penalties per game.
[tex]\[
\text{Average penalties per game} = \frac{10 \text{ penalties}}{4 \text{ games}} = 2.5 \text{ penalties per game}
\][/tex]
So, Meri gets an average of 2.5 penalties per game.
### Problem 2:
#### a. On a hike Deshawn walked 28 km in 7 hours. How long will it take him to walk 100 km?
1. First, let's find Deshawn's walking rate (km per hour).
[tex]\[
\text{Rate} = \frac{28 \text{ km}}{7 \text{ hours}} = 4 \text{ km per hour}
\][/tex]
2. Next, we need to determine how long it will take him to walk 100 km.
[tex]\[
\text{Time to walk 100 km} = \frac{100 \text{ km}}{4 \text{ km per hour}} = 25 \text{ hours}
\][/tex]
So, it will take Deshawn 25 hours to walk 100 km.
#### b. A grey whale's heart beats 24 times in 3 minutes. At this rate, how many times does it beat in one day?
1. First, let's find the whale's heart rate per minute.
[tex]\[
\text{Heart rate per minute} = \frac{24 \text{ beats}}{3 \text{ minutes}} = 8 \text{ beats per minute}
\][/tex]
2. Now, we need to calculate the number of times the heart beats in one day (24 hours).
1 day = 24 hours = 24 \times 60 = 1440 minutes
[tex]\[
\text{Heart beats in one day} = 8 \text{ beats per minute} \times 1440 \text{ minutes} = 11520 \text{ beats}
\][/tex]
So, the grey whale's heart beats 11520 times in one day.
All the results have been obtained step-by-step to ensure understanding of how to solve these types of problems using unit rates and proportions.
