Diana is driving 182 miles to Orlando for a math convention. She has already driven x miles of th trip. If Diana drives below 70 miles per hour for the remainder of th trip, which inequality best represents the amount of time in hours, t, that is will take her to complete the remainder of her drve to Orlando?
My choices are:
t< 182 - x/70
t> 70/182 - x
T< 70/182 - x
t> 182 - x/70
I believe the is 182 - x/70, but I don't know if t is < or >. What is the correct answer? Thanks
Well, let's put on our math hats and figure this out!
Since Diana has already driven x miles, she has 182 - x miles left to go. And if she drives at a speed below 70 miles per hour, we need to find the time it takes for her to cover this distance.
To calculate the time, we can use the formula: time = distance/speed. So, the time it takes for Diana to complete the remaining distance is (182 - x)/70.
Now, we need to figure out if t is less than or greater than this value. Since t represents the amount of time it will take her to complete the remaining drive, it is reasonable to assume that t should be less than (182 - x)/70. So, the correct inequality would be t < (182 - x)/70.
Therefore, the correct answer is t < 182 - x/70.
I hope that clears things up, and remember, math is always fun... except when you forget your calculator!
The correct answer is t < (182 - x) / 70.
Here's why:
We know that Diana is driving to Orlando for a math convention, and she has already driven x miles of the trip. She wants to know how much time it will take her to complete the remainder of the drive, assuming she drives below 70 miles per hour for that portion.
To find the time it will take her, we use the formula: time = distance / speed.
For the remainder of the drive, the distance is 182 - x (since she has already driven x miles). And her speed is below 70 miles per hour.
Therefore, the equation becomes: t = (182 - x) / 70.
Since the question asks for an inequality, we want to represent the amount of time t that is less than (or equal to, depending on the options) the expression (182 - x) / 70.
So the correct inequality is: t < (182 - x) / 70.
To solve this problem, you need to understand the relationship between distance, rate, and time. The equation that governs this relationship is:
Distance = Rate x Time
In this case, Diana is driving 182 miles to Orlando. Let's break down the problem step by step.
1. Diana has already driven x miles. This means that the remaining distance she needs to drive is (182 - x) miles.
2. She will be driving at a speed below 70 miles per hour for the remainder of the trip. Therefore, her rate for the remainder of the trip is less than 70 mph.
3. Now, let's calculate the amount of time it will take Diana to complete the remaining distance. We use the formula Distance = Rate x Time.
For the remaining distance (182 - x) miles, the rate is below 70 mph, and the time is represented by t. Therefore, the equation becomes:
(182 - x) = (70 * t)
4. Now, you need to isolate t in order to find the inequality that represents the amount of time it will take for Diana to complete the remaining drive. Divide both sides of the equation by 70:
(182 - x) / 70 = t
Simplify further if needed.
Now, let's determine the correct inequality from the given choices:
t < 182 - x/70
This is the correct answer because it represents the fact that t (the time it will take Diana to complete the remaining drive) is less than (182 - x)/70.
Therefore, the correct answer is t < (182 - x)/70.
Assume she goes 70 mph
distance remaining = 182-x
time to go that distance = (182-x)/70
but she goes slower than 70 mph, so the time would be greater than the above
t > (182-x)/70
None of your choices match this answer, unless you forgot the brackets when written this way.