Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer:
Step-by-step explanation:
Let \( x \) be Annette's average speed in mph.
First, calculate the time \( t \) taken to drive 70 miles at speed \( x \):
\[ t = \frac{70}{x} \]
Next, according to the problem statement, if her speed were increased by 6 mph, the new speed would be \( x + 6 \), and she would travel 84 miles in the same time \( t \):
\[ t = \frac{84}{x + 6} \]
Since both expressions represent the same time \( t \), we can set them equal to each other:
\[ \frac{70}{x} = \frac{84}{x + 6} \]
To eliminate the fractions, cross-multiply:
\[ 70(x + 6) = 84x \]
Expand and simplify the equation:
\[ 70x + 420 = 84x \]
\[ 420 = 84x - 70x \]
\[ 420 = 14x \]
Now, solve for \( x \):
\[ x = \frac{420}{14} \]
\[ x = 30 \]
Therefore, Annette's average speed was \( \boxed{30} \) mph.
To verify:
- At \( x = 30 \) mph, time taken to travel 70 miles:
\[ t = \frac{70}{30} = \frac{7}{3} \text{ hours} \]
- At \( x + 6 = 36 \) mph, time taken to travel 84 miles:
\[ t = \frac{84}{36} = \frac{7}{3} \text{ hours} \]
Both calculations confirm that \( t = \frac{7}{3} \) hours, verifying that the average speed of \( \boxed{30} \) mph is correct.
Answer:
Annette's average speed was 18 mph.
Step-by-step explanation:
To solve this problem, we can use the average speed formula, which is given by:
Average speed = Distance / Time
Given that Annette drives 70 miles at a certain speed, we can call this speed x. Thus, the time it takes her to travel 70 miles is 70/x.
If the average speed was 6 mph more, she could travel 84 miles in the same time. Therefore, the time to travel 84 miles at a speed of x + 6 would be 84/(x + 6).
As time is the same in both situations, we can equate the two time expressions:
70/x = 84/(x + 6)
Now, we can solve this equation to find the value of x, which will be Annette's average speed in mph.
Solving the above equation, we find that x = 18 mph.
Therefore, Annette's average speed was 18 mph.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
