Jane travels 3 times as fast as Eric. Traveling in opposite directions, they are 252 miles apart after 3 hours. Find their rates of travel

Let Jane's rate of travel be \( r_J \) and Eric's rate be \( r_E \). From the problem, we know the following:

1. Jane travels 3 times as fast as Eric: 
   \[
   r_J = 3r_E
   \]

2. After 3 hours, they are 252 miles apart, traveling in opposite directions. The total distance covered by both is the sum of the distances each person has traveled. The distance traveled by each person is given by \( \text{rate} \times \text{time} \).

So, the total distance traveled by Jane and Eric after 3 hours is:
\[
3r_J + 3r_E = 252
\]

Substitute \( r_J = 3r_E \) into the equation:
\[
3(3r_E) + 3r_E = 252
\]

Simplify:
\[
9r_E + 3r_E = 252
\]
\[
12r_E = 252
\]

Solve for \( r_E \):
\[
r_E = \frac{252}{12} = 21 \, \text{miles per hour}
\]

Now, find \( r_J \) using \( r_J = 3r_E \):
\[
r_J = 3 \times 21 = 63 \, \text{miles per hour}
\]

Thus, Eric's rate of travel is **21 miles per hour**, and Jane's rate of travel is **63 miles per hour**.

Would you like more details or have any questions?

Here are five related questions:
1. How far does Eric travel in 5 hours at his rate of 21 mph?
2. If Jane travels for 4 hours, how far will she go at her rate of 63 mph?
3. What is the total distance covered if they both travel for 6 hours in opposite directions?
4. What would happen if Jane and Eric were traveling in the same direction? How would that affect the equation?
5. If Eric increased his speed by 5 mph, how would this change the time it takes for them to be 252 miles apart?

**Tip:** When solving word problems involving distance, remember that distance equals rate times time, and adjust for directions accordingly!

Jane travels 3 times as fast as Eric. Traveling in opposite directions, they are 252 miles apart after 3 hours. Find their rates of travel.

Solve how Jane travels 3 times as fast as Eric and find their respective rates of travel when they are 252 miles apart after 3 hours. Learn how to apply the distance-rate-time relationship using linear equations. Suitable for students in Grades 7-9.

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