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

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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.