The time, t, required to travel a fixed distance varies inversely as the
rate of motion, r. if you travel 3 hours at a rate of 56 mph, then find the
rate you must travel for 4 hours,

You must travel at 42 mph for 4 hours

Solution:

Time varies inversely as rate of motion

Let "t" be the time required

Let "r" be the rate of motion

Then, we get

Where, "k" is the constant of proportionality

You travel 3 hours at a rate of 56 mph

Substitute t = 3 and r = 56 in eqn 1

Find the  rate you must travel for 4 hours

r = ? and t = 4

Substitute t = 4 and k = 168 in eqn 1

Thus you must travel at 42 mph for 4 hours