# act 1874fpre answer key

## If a car were to be traveling at a rate of 55 miles per hour and it were to travel 155 miles, how long would it take the car to travel the 155 miles?

This is a pretty straightforward problem. First, you need to figure out what speed the car is traveling at, which is 55 miles per hour. Then, you need to figure out how many hours it will take for the car to travel 155 miles. You can do this by using the formula: distance = speed * time. Using this formula with our information from before, we have:

155 = 55(time), so divide both sides by 55 and we get 2.8 hours on one side and 155 on the other side of the equation.

This equals 2 hours and 48 minutes or 2 hours and 1 minute (3 hours).

## 3 hours and 1 minute

#1) Calculate the area of a triangle by drawing lines from the vertex opposite the angle to the side farthest away from it.

#2) The area of a triangle is the length of its base multiplied by ____________.

#3) Add these two together to get your answer.

## If it took you 5 hours and 55 minutes to drive 300 miles and you drove an average speed of 50 miles per hour, how far would you need to travel in order to drive 500 miles?

The problem is asking you to find the complexity of an algorithm.

To solve this problem, use the following steps:

- You drive 300 miles in 5 hours and 55 minutes at an average speed of 50 miles per hour
- Divide the time spent driving by the number of miles driven to get your time constant: 5 hours and 55 minutes / 300 miles = 1/60 hour per mile (you can simplify this fraction by dividing both numerator and denominator by 5)
- To drive 500 miles, take your time constant and multiply it by 500: 1/60 * 500 = 50/3 hours or about 16 2/3 hours
- The last 200 miles of your trip will take about 8 1/3 extra hours on top of the initial 5 hours and 55 minutes

## 200 miles

- 200 miles

## If a car travels at a rate of 20 miles per hour for 5 hours, how far will the car have traveled?

It is important to note that when working with rates, the time unit must be homogeneous. An hour can’t be converted into a fraction of an hour because it isn’t consistent. If you have miles divided by hours, you need to make sure the hours are all expressed in terms of the same type of hour. Therefore, we’ll express 5 hours as 300 minutes. We can multiply our rate by 300 minutes to determine how far the car will travel in 5 hours:

20 mph * 300 min = 6000 mi/hr

## 100 miles

Imagine you are traveling in a car at 20 miles per hour.

If you travel for 5 hours, how many miles will you go?

Show that the answer is 100 miles by completing the following solution:

## If it takes 6 hours for a plane to fly 500 miles, and if the plane flies at a constant speed the entire time, what is the average speed of the plane in miles per hour?

For the first question, solve for average speed like this:

`(average speed) = (distance)/(time)`

You can also write it as: `d/t = s`. This is known as an equation. In the equation above, `s` denotes `speed`, `d` denotes `distance`, and `t` denotes time. For this problem, we know the distance and time, so we’ll solve for average speed.

## 83.3 mph

The correct answer is 83.3 mph

Here’s how to get it:

Average speed is the distance traveled divided by the time taken. As we do not know the actual distance traveled, we can use the given formula instead: Speed = Distance/Time

By substituting the values, we get: 30mph = (Distance)/2hrs or 60mph = (Distance)/1hr. So if we set these two equations equal to one another and subtract them, we will find out how much farther she must travel in 1 hour at 60mph than she would have in 2 hours at 30mph. That extra amount of distance is what puts her average speed at 83.3 mph for the entire trip.

30(Distance) = 60(Distance) – (Distance)/2

30(Distance) – 120(Distance) + (Distance)/2 = 0 … Divide each side by (distance), which cancels out on both sides and leaves us with our answer:

- 90 miles + .5 miles = 90.5 miles

Now that you’ve solved for this unknown value of your original equation, you can solve for any other unknown value using your original equation as well!

## An airplane travels at an average speed of 500 mph with no wind. How long will it take for this airplane to travel 2000 mi?

Answer: The plane will arrive in 4 hours.

To calculate this, you can use the formula d = st, where d is distance, s is speed and t is time. Let’s plug in the numbers we know:

d = 500 mph x 4 h = 2000 mi

Since the original question was asking for time (not distance), we have to rearrange the equation so that it reads t = d / s. Notice that while we did not know what “t” was at first, because we solved for “t” earlier in this problem, we now know what t equals, so our answer is all set!

This math technique can also be done using an online calculator as shown below. Again notice how units are important here! Since our given values were measured in mph and miles respectively, our answer should be measured in hours!

## 4 hours

- How far did the car travel?

Use the formula d=r*t.

- If the speed is constant, you can find the distance traveled by multiplying time (t) by rate (r).
- For example, if your car travels at a speed of 55 miles per hour for 4 hours, how far does it travel?
- Convert everything to hours if necessary. In this case, we don’t need to convert because we are given that the car travels at 55 mph for 4 hours.
- Plug in values into d = r * t:
- d = 55 * 4 = 220 miles.

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