The time t required to drive a certain distance varies inversely with the speed r. If it takes 4 hours to drive the distance at 35 miles per hour, how long will it take to drive the same distance at 45 miles per hour?
A. about 3.11 hours
B. 140 hours
C. about 5.14 hours
D. 393.75 hours
The inverse variation equation is $tr=k$, where $k$ is a constant. We can solve for $k$ using the given information: $4\cdot35=k \Rightarrow k=140$. Thus, the equation for this situation is $tr=140$. To find the time required to drive the same distance at 45 miles per hour, we substitute $r=45$ and solve for $t$: $t\cdot45=140 \Rightarrow t \approx 3.11$. Therefore, the answer is $\boxed{\textbf{(A)}\ \text{about 3.11 hours}}$.
re-answer that
Sure, here's the re-answer:
The inverse variation equation is $tr=k$, where $k$ is a constant. We can solve for $k$ using the given information: $4\cdot35=k \Rightarrow k=140$. Thus, the equation for this situation is $tr=140$. To find the time required to drive the same distance at 45 miles per hour, we substitute $r=45$ and solve for $t$: $t\cdot45=140 \Rightarrow t \approx 3.11$. Therefore, the answer is $\boxed{\textbf{(A)}\ \text{about 3.11 hours}}$.
To solve this problem, we can use the formula for inverse variation:
t = k/r
where t is the time, r is the speed, and k is the constant of variation.
We are given that it took 4 hours to drive the distance at a speed of 35 miles per hour. We can use this information to find the value of k.
4 = k/35
To solve for k, we can cross multiply:
k = 4 * 35
k = 140
Now, we can use the value of k to find the time it will take to drive the same distance at 45 miles per hour.
t = 140/45
t ≈ 3.11 hours
Therefore, the correct answer is A. about 3.11 hours.