can you please show me the steps for this word problem? in need to write the inequality and solve. how long will Kenzie drive if she averages 55mph and wants to complete at least 440 mi. of her trip?
1) You've been given a speed, and a distance, and you must find a time. So first, identify the formula that relates the three, which is: speed x time = distance
2) Taking the unknown time as x (in hours, since the speed is given in hours), plug the values into the formula
=> 55x = 440
3) The problem says that she would like to complete AT LEAST 440 miles, which means she could also cover a greater distance. Thus, the left side of the equation could also be greater than 440.
=> 55x >= 440
4) Now you can divide by 55 on both sides to obtain the inequality for x.
please let me knoe if this is correct 55/55 + > 440/5 t=8. is it written correctly please show me if not thats where my problem comes
55t => 440.
t => 440/55
t => 8 Hours.
Certainly! To solve this word problem, you will need to write and solve an inequality.
Step 1: Define the variables
Let's define the variables:
- d: the distance Kenzie will drive.
- r: the average speed in miles per hour (mph) Kenzie will be driving.
- t: the time it takes for Kenzie to drive the distance d.
Step 2: Write the inequality
The inequality to represent the given situation is:
d ≥ 440
This inequality states that Kenzie needs to drive a distance of at least 440 miles.
Step 3: Relate distance, speed, and time
The formula that relates distance, speed, and time is:
distance = speed × time
In this case, the distance is represented by d, the speed is represented by r, and the time is represented by t. So we can write:
d = r × t
Step 4: Rearrange the formula
Since we want to find the time, t, in terms of the distance, d, and speed, r, we rearrange the formula from step 3:
t = d / r
Step 5: Substitute the given values and solve
Now, substitute the average speed, r = 55 mph, and the minimum distance, d = 440, into the formula:
t = 440 / 55
t = 8
Therefore, Kenzie will drive for at least 8 hours to complete a trip of at least 440 miles, given that she averages a speed of 55 mph.