The problem in the image asks:

The distance one travels varies directly with the time spent traveling at a constant rate of speed. It took 11 hours for Brendan to drive 55 miles. In 6 hours, how far can he go?

We are given that distance varies directly with time. This means the relationship between distance ($d$) and time ($t$) can be described by a direct proportion:

$d = k \cdot t$

Where:

• $d$ is the distance traveled,
• $t$ is the time,
• $k$ is the constant of proportionality (which represents the rate of travel).

Step 1: Find the rate of travel (constant $k$)

It took Brendan 11 hours to travel 55 miles. So we can substitute this information into the formula:

$55 = k \cdot 11$

Solving for $k$:

$k = \frac{55}{11} = 5$

So, Brendan's rate of travel is 5 miles per hour.

Step 2: Use the rate to find the distance in 6 hours

Now that we know the rate of travel ($k = 5$), we can find how far Brendan can travel in 6 hours by substituting into the formula:

$d = 5 \cdot 6 = 30$

Thus, Brendan can travel 30 miles in 6 hours.

The correct answer is B) 30 miles.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. If Brendan traveled for 8 hours, how far would he go?
2. If Brendan increased his speed and could travel 66 miles in 6 hours, what would his new rate of travel be?
3. How long would it take Brendan to travel 150 miles at his current rate?
4. If another person travels 80 miles in 10 hours, what is their rate of travel?
5. What would happen to the distance if the time was tripled?

Tip: In direct variation problems, once you know the rate (constant of proportionality), solving for other values becomes straightforward by plugging the known values into the formula.