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 (1)/(r)\\\\t = k * (1)/(r)\\\\t = (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 = (k)/(56)\\\\k = 3 * 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 = (168)/(r)\\\\r = (168)/(4)\\\\r = 42`

Thus you must travel at 42 mph for 4 hours