Question

In terms of T, what is the number of hours travelling on country roads?

Answer 1

From the time information: `4-T` hours.

Using the speed and distance information: `30/7-9/7T` hours.

Solving: `T=1` and time on country roads is `3` hours.

Explanation:

The question is confusing in that there are two ways to find such a formula. However, that does allow you to derive an equation in `T` which can then be solved...

Formula based on time information given

We are told that the journey took `4` hours, of which `T` hours was on the freeway and the remainder was on country roads.

So the time on country roads was:

`4-T` hours

Formula calculated from distances and speeds

The distance travelled on the freeway is `90T` km.

So the distance travelled on country roads is `300 - 90T` km.

The time taken to travel that distance is given by dividing by the average speed, to get:

`(300-90T)/70 = (30-9T)/7 = 30/7-9/7T` hours.

Solve for `T`

Given these two formulae which should give the same result, we can write:

`4 - T = 30/7-9/7T`

Add `9/7T-4` to both sides to get:

`2/7T = 2/7`

So `T=1`

That is, a total of `1` hour was spent on the freeway and `3` hours on country roads.