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Annette drives her car 70 miles and has an average of a certain speed. If the average speed had been 6 mph more, she could have traveled 84 miles in the same length of time. What was her average speed?

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.