Question

The time (t) of travel on an automobile trip varies inversely as the speed (v) of the automobile, Traveling at an average speed of 65 mph, a trip took 3 h. The return trip took 5 h. Find the average speed on the return trip.

Answer 1

We can use the formula for inverse variation to solve the problem:

t = k/v

where t is the time of travel, v is the speed, and k is a constant of proportionality.

We know that when traveling at an average speed of 65 mph, the trip took 3 hours. So we can set up an equation:

3 = k/65

Solving for k, we get:

k = 195

Now, we want to find the average speed on the return trip when the time of travel was 5 hours. We can set up another equation:

5 = 195/v

Solving for v, we get:

v = 39 mph

So the average speed on the return trip was 39 mph.

Answer 2

the average speed on the return trip was 39 mph.

Explanation:

Let's call the average speed on the return trip "v". We know that the time of travel (t) is inversely proportional to the speed (v), so we can write:

t = k/v

where k is a constant of proportionality.

We can use the information given to find the value of k. We know that when the average speed is 65 mph, the trip takes 3 hours. So we have:

3 = k/65

To solve for k, we can multiply both sides by 65:

k = 195

Now we can use this value of k to find the average speed on the return trip. We know that the time for the return trip is 5 hours, so we can write:

5 = 195/v

To solve for v, we can multiply both sides by v:

5v = 195

Dividing both sides by 5, we get:

v = 39

Therefore, the average speed on the return trip was 39 mph.