20. The time t required to drive a certain distance varies inversely with the speed, r. If it takes 2 hours to drive the distance at 67 miles per hour, how long will it take to drive the same distance at 55 miles per hour?

t = k/r

2 = k/67
k = 134 (which happens to be the distance)

t = 134/r
t = 134/55
t = 2.436 hours

2.45?

yes

THANK YOU

THANKS BRUH!!!!!!!!!!!!

Why did the car take a break during the math exam? Because it needed some time to solve its own equations!

To solve this problem, we can use the inverse variation formula: t = k/r, where t is the time, r is the speed, and k is a constant. We can use the given information to find k.

If it takes 2 hours to drive the distance at 67 miles per hour, we can substitute these values into the formula: 2 = k/67. Solving for k, we find k = 2 * 67 = 134.

Now we can use the value of k to find the time it takes to drive the same distance at 55 miles per hour: t = 134/55. Calculating this, we get t ≈ 2.44 hours.

So, the answer is approximately 2.44 hours, which is closest to option c.

To solve this problem, we can use the inverse variation formula. Inverse variation means that one quantity decreases as the other quantity increases.

The formula for inverse variation is:

t = k/r

Where:
t is the time taken to drive the distance,
k is the constant of variation,
and r is the speed.

We are given that it takes 2 hours to drive the distance at 67 miles per hour. We can plug these values into the formula to find the constant of variation:

2 = k/67

To solve for k, we can cross multiply:

2 * 67 = k
k = 134

Now that we have the constant of variation, we can use it to find the time taken to drive the distance at 55 miles per hour. Let's call this time t2:

t2 = k/r2

Substituting the values, we get:

t2 = 134/55

Calculating the value, we find:

t2 ≈ 2.43636 hours

Rounding to two decimal places, the answer is approximately 2.44 hours.

Therefore, the correct answer is c. about 2.45 hours.