Question

Paul and Eve start from the same place at the same time and walk in opposite directions on Oak Drive. Eve walks twice as fast as Paul. After 30 minutes they are 24 blocks apart. how far does Paul walk?

Answer 1

Answer:

8

Step-by-step explanation:

The distance between them (24) is the distance paul walked plus the distance eve walked.

Let the distance paul walked be x. Then the distance eve walked is 2x. this is because distance = speed * time. In the same amount of time (30 minutes in this case), the person with twice the speed will go twice the distance.

Now, x + 2x =24

3x = 24

x = 8

Answer 2

Answer:

Paul walks 8 blocks.

Step-by-step explanation:

Let P be Paul's waking speed (in blocks per minute).

Let E be Eve's waking speed (in blocks per minute).

Since Eve walks twice as fast as Paul, we can express Eve's speed in terms of Paul's speed as:

$\sf E = 2P$

Now, let's consider the distance each person covers in 30 minutes, remembering that distance is the product of speed and time:

$\sf Paul's\; distance = P \times 30 = P30\;blocks$

$\sf Eve's\; distance = E \times 30 = E30\;blocks$

The total distance between Paul and Eve after 30 minutes is the sum of the distances they have covered:

$\sf 30P + 30E = 24$

Now, substitute E = 2P into the equation, and solve for P:

$\sf 30P + 30(2P) = 24$

$\sf 30P + 60P = 24$

$\sf 90P = 24$

$\sf P = \dfrac{24}{90}$

$\sf P = \dfrac{4}{15}$

So, Paul's walking speed is 4/15 blocks per minute.

To find how far Paul walks, multiply his speed by the time (30 minutes):

$\textsf{Distance walked by Paul} =\sf \dfrac{4}{15} \times 30 =8\;blocks$

Therefore, Paul walks 8 blocks.