t = k/r
2 = k/67
k = 134 (which happens to be the distance)
t = 134/r
t = 134/55
t = 2.436 hours
a. about 1.64 hours
b. about 134.00 hours
c. about 2.45 hours
d. about 61.00 hours
Please help! I'm working on my final math exam!
2 = k/67
k = 134 (which happens to be the distance)
t = 134/r
t = 134/55
t = 2.436 hours
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.
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.