Question

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,

Answer 1

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

$t \propto \frac{1}{r}\\\\t = k \times \frac{1}{r}\\\\t = \frac{k}{r} -------- eqn 1$

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

$3 = \frac{k}{56}\\\\k = 3 \times 56\\\\k = 168$

Find the  rate you must travel for 4 hours

r = ? and t = 4

Substitute t = 4 and k = 168 in eqn 1

$4 = \frac{168}{r}\\\\r = \frac{168}{4}\\\\r = 42$

Thus you must travel at 42 mph for 4 hours