Going Round-Trip with the World’s Fastest Land Animal

Going Round-Trip with the World’s Fastest Land Animal

According to the Travel Almanac, the world’s fastest land animal is the cheetah. It can travel at up to 70 mph. Think of this scenario: A cheetah sitting under a tree sprints toward its prey at 70 mph. It runs back to its initial spot by the tree at a modest 40 mph. The cheetah has embarked on a round-trip. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.

Can we say that this cheetah’s average rate was 55 mph?

That’s one of the things you’ll determine as you work to complete this task. Make a conjecture. What do you think the answer will be?

Directions:

Complete each of the following tasks, reading the directions carefully as you go. Be sure to show all work where indicated and to insert images of graphs when needed. Make sure that all graphs or screenshots include appropriate information, such as titles and labeled axes. If your word processing program has an equation editor, you can insert your equations here. Otherwise, print this activity sheet and write your answers by hand.

You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all of your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations.

Your teacher will give you further directions as to how to submit your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy.

Before you begin, recall the formula that relates distance, rate, and time.

The distance formula is given by d = rt, where:

        d represents distance. Common units are miles or feet.

        t represents time. Common units are hours or seconds.

        r represents rate or velocity. Common units are miles per hour or feet per second.

You can calculate distance by finding the product of an average rate of an object traveling and the duration of time for which it travels. Remember, units for distance and time must agree with the units for rate.

Now let’s get started!

Step 1: Calculating distance at maximum speed

If the cheetah sprinted at maximum speed, how far would the cheetah have traveled?

1. Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.

D=tmin *1.1667miles

1. Let t = 10 and solve for the distance the cheetah covered in 10 minutes.

D=11.667miles

Step 2: Calculating distance using varied speeds

Suppose the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes.

1. How far would the cheetah have traveled in the first 8 minutes? Show how you arrived at your answer.

D=9.3336miles

1. How far would the cheetah have traveled in the next 8 minutes? Show how you arrived at your answer.

D=5.3miles

1. How much farther did the cheetah travel in the first 8 minutes than in the second 8 minutes?

4.0336

1. The cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. Was the distance traveled during the first 8 minutes 1.75 times greater than the distance traveled during the second 8 minutes? Show the calculation to justify your answer.

The first 8 mins was 1.75 times faster than the second 8 mins. 1.75*5.3=9.275 (compared to 9.3336) which is close enough considering slight rounding of numbers.