Answer :
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.
