For this exercise we can write and graph a system of inequalities. The system will have three inequalities.

Inequality (I) represents the total amount of time driving by us and our friend.
Inequality (II) represents the distance covered given speed and time.
Inequality (III) represents the fact that our friend drives more hours than us.

For all three inequalities we will let $x$ represent the number of hours we drive and $y$ represent the number of hours our friend drives.

Writing the Inequalities

Inequality (I): It is given that we plan to drive less than 15 hours. We can write an inequality to represent this situation in the following way.

x + y < 15

Inequality (II): It is given that we drive

70

mph and our friend drives

60

mph. The phrase at least can be interpreted as greater than or equal to and represented with

\geq .

Then, we have the following inequality.

70 x + 60 y \geq 600

Inequality (III): It is given that our friend drives more than us. We can write the following equality.

y > x

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