Let's work through each part of the problem step by step.

(a) Solve the formula for $t$:

We start with the formula for distance: $d = rt$

To solve for $t$, we need to isolate $t$ on one side of the equation. We can do this by dividing both sides of the equation by $r$ (assuming $r \neq 0$):

$t = \frac{d}{r}$

So, the formula for time is: $t = \frac{d}{r}$

(b) Use the formula in part (a) to find the time that you travel if you cover a distance of 150 miles at an average rate of 60 miles per hour.

Using the formula $t = \frac{d}{r}$, we can substitute the values given in the problem:

• $d = 150$ miles (distance traveled)
• $r = 60$ miles per hour (average rate)

Substituting into the formula: $t = \frac{150}{60} = 2.5 \text{ hours}$

Thus, it takes 2.5 hours to travel 150 miles at an average rate of 60 miles per hour.

Summary:

• (a) The formula for time is $t = \frac{d}{r}$.
• (b) It takes 2.5 hours to travel 150 miles at 60 miles per hour.

Would you like more details or have any questions?

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Here are 5 related questions that expand on this concept:

1. If you travel 120 miles in 3 hours, what is your average speed?
2. How long will it take to travel 300 miles at 50 miles per hour?
3. If you decrease your speed to 40 miles per hour, how long will it take to cover 80 miles?
4. If you travel 200 miles at a speed of 75 miles per hour, how much time will it save compared to traveling at 60 miles per hour?
5. What distance would you cover in 4 hours at a speed of 55 miles per hour?

Tip: Always keep track of the units when working with rate, time, and distance problems, and ensure they are consistent.