Question

On a road trip with a friend, you drive about 70 miles per hour, and your friend drives about 60 miles per hour. The plan is to drive less than 15 hours and at least 600 miles each day. Your friend will drive more hours than you. How many hours can you and your friend each drive in 1 day?

Responses
-you drive 4 hours; your friend drives 5 hours
-you drive 6 hours; your friend drives 6 hours
-you drive 6 hours; your friend drives 8 hours
-you drive 7 hours; your friend drives 8 hours

Answer 1

I drive for 0 hours and my friend drives for 10 hours.

Explanation:

Given that me and my friend are on a road trip. My speed is 70 miles per hour and my friend's speed is 60 miles per hour. Our plan is to drive less than 15 hours and at least 600 miles each day.

Also, my friend will drive more hours than me.

Let, 'x' and 'y' be the number of hours drove by me and my friend respectively. Then, according to the given information, we have the following inequalities.

`y > x`

`x + y < 15`

`70x + 60y \geqslant 600`

When we plot these inequalities in a graph paper, we can see in the attached figure, where the common shaded region gives the solution set, one of the solutions is point 'P', given by

x = 0 and y = 10.

This solution satisfies all the three conditions given above.

Thus, one of the solutions is -

I will drive for O hours and my friend will drive for 10 hours.