Question

Lovish has $6$ hours to spend in Ha Ha Tonka State Park. He plans to drive around the park at an average speed of $20$ miles per hour, looking for a good trail to hike. Once he finds a trial he likes, he will spend the remainder of his time hiking it. He hopes to travel more than $60$ miles total while in the park. If he hikes at an average speed of $1.5$ miles per hour, which of the following systems of inequalities can be solved for the number of hours Lovish sends driving d, and the number of hours he spends hiking, h while he is at the park?

• A. $1.5h+20d>60,h+d\le 6$
• B. $1.5h+20d>60,h+d\ge 6$
• C. $1.5h+20d<0,h+d\ge 360$
• D. $20h+1.5d>6,h+d\le 60$

Answer 1

The correct option is A $1.5h+20d>60,h+d\le 6$

Given that Lovish has spend $6$ hours in Ha Ha park.

He drives around the park at an average speed of $20$ miles per hours

And he will spend the reminder time by hiking if hikes an avarge speed of $1.5$ miles per hours.

If he spend $d$ hours for drives and $h$ hours for hiking.

He hopes to travel more than total $60$ miles run in park

Then he traveldistance in driving $=20d$ miles

And he travel distance in hiking $=1.5$h

Then total distance travel by Lovish in park $=1.5h+20d$

And total time spend by Lovish in park $=h+d$

But given that Lovish travels $60$ miles in park by spending $6$ hours.

$\therefore h+d\le 6$

$\therefore 1.5h+20d>60$