Question

The formula \(d=50 t\) determines the distance, in miles, that a car travels in \(t\) hours at a steady speed of 50 miles per hour. a. Complete a table of values for the input values: \(t=0,1,2,3,4,\) and 5 hours. b. Plot the input/output pairs from the table in part a on the following grid. Choose uniform scales on each axis that will allow you to clearly plot all your points. c. How long does it take to travel 200 miles?

Short answer

Answer: It takes 4 hours to travel 200 miles at a constant speed of 50 miles per hour.

Step-by-step solution

Identify the formula for distance

The given formula is \(d=50t\), where \(d\) represents the distance in miles, and \(t\) represents the time in hours.

Complete the table of values

Using the formula and the input values (time) \(t=0,1,2,3,4,\) and 5 hours, calculate the output values (distance). Time(t) | Distance(d) --------|----------- 0 | 50*0 = 0 1 | 50*1 = 50 2 | 50*2 = 100 3 | 50*3 = 150 4 | 50*4 = 200 5 | 50*5 = 250 Here is the completed table: Time(t) | Distance(d) --------|----------- 0 | 0 1 | 50 2 | 100 3 | 150 4 | 200 5 | 250

Plot the input/output pairs on the grid

With uniform scale on both axes, plot the input/output pairs (time, distance) from the table: (0,0) (1,50) (2,100) (3,150) (4,200) (5,250) Place a point at each coordinate on the grid. Adjust the scale as needed to fit all points, and connect the points to create a line.

Find the time to travel 200 miles

The formula for distance is \(d=50t\). To find the time to travel 200 miles, set the distance \(d\) to 200 and solve for \(t\): \(200 = 50t\) Divide both sides by 50: \(t = \frac{200}{50}\) \(t = 4\) hours Thus, it takes 4 hours to travel 200 miles.