To solve the problem, we start by using the formula for inverse variation, which states that if \( t \) varies inversely with \( r \), we can express this relationship as:
\[ t \cdot r = k \]
where \( k \) is a constant.
From the information given, we know that it takes 2 hours to drive the distance at 30 miles per hour. We can calculate the constant \( k \):
\[ k = t \cdot r = 2 , \text{hours} \cdot 30 , \text{miles per hour} = 60 \]
Now, we want to find out how long it takes to drive the same distance at 35 miles per hour. We use the same formula:
\[ t \cdot r = k \]
Substituting \( r = 35 , \text{miles per hour} \) and \( k = 60 \):
\[ t \cdot 35 = 60 \]
Now, we can solve for \( t \):
\[ t = \frac{60}{35} \]
Calculating the above expression:
\[ t = \frac{60}{35} = \frac{12}{7} \approx 1.714 , \text{hours} \]
Thus, the approximate time it will take to drive the same distance at 35 miles per hour is about 1.71 hours.
The answer is about 1.71 hours.
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