1. The time t that it takes for a salesman to drive a certain distance d varies inversely as the average speed r. It takes the salesman 4.75 h to travel between two cities at 50 mi/h.


How long would the drive take at 50 mi/h?

t=k/r

4.75=k/50 or k= 4.75*50

To find the answer, first, we need to set up the relationship between time, speed, and distance using the formula for inverse variation:

t = k/r

where t is the time, r is the average speed, and k is a constant of variation.

Next, we can use the information provided to find the value of k. We are given that it takes the salesman 4.75 hours to travel a distance. We are also given that the average speed is 50 mi/h. Plugging these values into the formula, we get:

4.75 = k/50

To find the value of k, we can cross multiply:

4.75 * 50 = k
237.5 = k

Now that we know the value of k, we can use it to answer the question. We are asked to find the time it would take to drive the distance at a speed of 50 mi/h. Plugging the values into the formula:

t = 237.5/50
t = 4.75 hours

Therefore, the drive would take 4.75 hours at a speed of 50 mi/h.

To find out how long the drive would take at 50 mi/h, we need to set up the inverse variation equation using the given information.

Let's start by defining the variables:
t = time to travel the distance (in hours)
d = distance between the two cities (in miles)
r = average speed of the salesman (in mi/h)

According to the problem, the time t varies inversely with the average speed r. This can be expressed as:

t = k/r

where k is the constant of variation.

We also know that it takes the salesman 4.75 h to travel between the two cities at 50 mi/h. So we can set up an equation using this information:

4.75 = k/50

To solve for k, we multiply both sides of the equation by 50:

4.75 * 50 = k
k = 237.5

Now that we have the value of k, we can use it to find the time it would take to travel at 50 mi/h:

t = 237.5/50
t = 4.75 hours

Therefore, the drive would still take 4.75 hours at 50 mi/h.

3.96 h