An airplane traveled a distance d in t hours, where r>1, and arrived one hour late. The airplane would have arrived on time if it had traveled at what rate per hour?

a. t-1
b. d/t-1
c. d/t+1
d. d/t-1
e. d/t+1

speed = distance/time.

its speed was d/t
on time its time would have been 1 hour less, so its speed would be d/(t-1)

To solve this problem, we need to determine the rate at which the airplane would have needed to travel to arrive on time.

Given:
Distance traveled = d
Time taken = t
Rate of travel = r

We know that the airplane arrived one hour late, so we can subtract 1 from the total time taken:
Total time taken = t + 1

To find the rate at which the airplane would have needed to travel to arrive on time, we can divide the distance traveled by the adjusted time taken:
Rate per hour = d / (t + 1)

Therefore, the correct answer is e. d / (t + 1).

To solve this problem, we need to determine the rate at which the airplane would have had to travel in order to arrive on time.

We know that the airplane traveled a distance d in t hours and arrived one hour late. So, if the airplane had arrived on time, it would have taken t-1 hours to travel the same distance d.

The rate of travel is the distance divided by the time taken. Therefore, the rate per hour at which the airplane would have had to travel to arrive on time is d divided by t-1.

Looking at the answer choices, we can see that option d. d/t-1 matches our calculated answer. Therefore, the correct answer is d. d/t-1.