There are 20 students in Joey’s PE class who are participating in an extracurricular walkathon to raise money for a field trip. The students are divided into two groups and each group is walking in opposite directions from the other group. Joey is the fastest student in his group and Natasha is the fastest student in her group. At the end of 2 hours, Natasha is about 4 km ahead of Mark who is the second fastest person in her group. On average, Joey walks about 2 km/hr faster than Natasha. The students will earn $1.50 per kilometer. If Mark earns $33. How much more does Joey earn than Natasha?

To find out how much more Joey earns than Natasha, we need to calculate the distance each of them walks and then multiply it by the earning rate.

Let's start by finding the distance Natasha walks in 2 hours. We know that she is about 4 km ahead of Mark, who is the second fastest person in her group. Since Mark is in the same group as Natasha, we can assume that Natasha is the fastest in her group. Therefore, Mark's distance is the same as Natasha's distance minus 4 km.

Let's denote Natasha's distance as "x" km. So Mark's distance would be "x - 4" km.

Now, we know that Joey walks about 2 km/hr faster than Natasha. Since we are given the time of 2 hours, we can calculate Joey's distance by multiplying his speed by the time. Let's denote Joey's speed as "y" km/hr. So Joey's distance would be "2y" km.

We also know that there are 20 students in Joey's PE class participating in the walkathon. Since they are divided into two groups, each group would have 10 students. Therefore, Natasha's group also has 10 students.

Now, let's calculate the total distance walked by Natasha's group. Since there are 10 students in the group, the total distance would be 10 times Natasha's distance, which is 10x km.

Similarly, let's calculate the total distance walked by Joey's group. Since there are 10 students in the group, the total distance would be 10 times Joey's distance, which is 10(2y) km.

We know that the earning rate is $1.50 per kilometer. So to find out how much each student earns, we need to multiply their respective distances by$1.50.

Now, let's calculate the earnings of Mark. Since Mark's distance is "x - 4" km, his earnings would be (x - 4) * $1.50.

To find out how much Joey earns, we need to calculate his distance first. Joey's distance is 2y km, so his earnings would be (2y) * $1.50.

We are given that Mark earns $33. So we can set up the equation:

(x - 4) * $1.50 =$33

Now, we can solve this equation to find the value of x.

Once we have the value of x, we can substitute it back into the equation for Joey's earnings to find out how much he earns.

Finally, to find out how much more Joey earns than Natasha, we subtract Natasha's earnings from Joey's earnings.

To find out how much more Joey earns than Natasha, we need to calculate the distance each of them walks and then multiply it by the earning rate.

Let's start by finding the distance Natasha walks in 2 hours. We know that she is about 4 km ahead of Mark, who is the second fastest person in her group. Since Mark is in the same group as Natasha, we can assume that Natasha is the fastest in her group. Therefore, Mark's distance is the same as Natasha's distance minus 4 km.

Let's denote Natasha's distance as "x" km. So Mark's distance would be "x - 4" km.

Now, we know that Joey walks about 2 km/hr faster than Natasha. Since we are given the time of 2 hours, Joey's distance would be 2 km/hr * 2 hr = 4 km more than Natasha's distance.

Therefore, Joey's distance would be "x + 4" km.

Now, let's calculate the earnings for each student. The earning rate is $1.50 per kilometer.

Natasha's earnings would be x km * $1.50/km =$1.50x.

Mark's earnings would be (x - 4) km * $1.50/km =$1.50(x - 4).

Joey's earnings would be (x + 4) km * $1.50/km =$1.50(x + 4).

We are given that Mark earns $33. So we can set up the equation:

$1.50(x - 4) =$33.

Now, let's solve for x:

1.50x - 6 = 33.

1.50x = 39.

x = 26.

Now that we have found the value of x, we can substitute it back into the equations to find the earnings for Natasha and Joey.

Natasha's earnings = $1.50(26) =$39.

Joey's earnings = $1.50(26 + 4) =$1.50(30) = $45.

To find out how much more Joey earns than Natasha, we subtract Natasha's earnings from Joey's earnings:

$45 -$39 = $6.

Therefore, Joey earns $6 more than Natasha.

To find out how much more Joey earns than Natasha, we need to calculate the distance each of them walks and then multiply it by the earning rate.

Let's start by finding the distance Natasha walks in 2 hours. We know that she is about 4 km ahead of Mark, who is the second fastest person in her group. Since Mark is in the same group as Natasha, we can assume that Natasha is the fastest in her group. Therefore, Mark's distance is the same as Natasha's distance minus 4 km.

Let's say Natasha's distance is D km. Mark's distance would then be D - 4 km.

Now, we know that Joey walks about 2 km/hr faster than Natasha. So, Joey's speed is Natasha's speed + 2 km/hr.

Since we have the time (2 hours) and the speed, we can calculate the distance Joey walks in 2 hours. Let's call it J km.

Now, we can calculate the earnings for each student. The earning rate is $1.50 per kilometer.

Natasha's earnings would be D km multiplied by $1.50/km.

Mark's earnings would be (D - 4) km multiplied by $1.50/km.

Joey's earnings would be J km multiplied by $1.50/km.

We are given that Mark earns $33. So, we can set up the equation:

(D - 4) km * $1.50/km =$33

Now, we can solve this equation to find the value of D.

Once we have the value of D, we can calculate Joey's earnings by multiplying J km by $1.50/km.

Finally, to find out how much more Joey earns than Natasha, we subtract Natasha's earnings from Joey's earnings.

I hope this helps! Let me know if you have any further questions.