Question

1. jessica left the science museum and traveled toward the lake at an average speed of 65 km/h. castel left two hours later and traveled in the opposite direction with an average speed of 65 km/h. how long does castel need to travel before they are 520 km apart?

Explanation:

Step1: Define variables

Let \( t \) be the time (in hours) that Castel travels. Then Jessica travels for \( t + 2 \) hours.

Step2: Calculate distance traveled by each

The distance formula is \( d = vt \), where \( v \) is speed and \( t \) is time.

• Jessica's distance: \( d_J = 65(t + 2) \)
• Castel's distance: \( d_C = 65t \)

Step3: Set up the equation

Since they are moving in opposite directions, the sum of their distances is 520 km. So:

$$ 65(t + 2) + 65t = 520 $$

Step4: Simplify and solve for \( t \)

First, expand the left side:

$$ 65t + 130 + 65t = 520 $$

Combine like terms:

$$ 130t + 130 = 520 $$

Subtract 130 from both sides:

$$ 130t = 520 - 130 = 390 $$

Divide both sides by 130:

$$ t = \frac{390}{130} = 3 $$

Answer:

3 hours