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

enter image source here

1 Answer
Jan 29, 2018

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.