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During a family trip, you share the driving with your dad. At most, you are allowed to drive for three hours. While driving, your maximum speed is 55 miles per hour.


Part A) Write a system of inequalities describing the possible numbers of hours “t” and distance “d” you may have to drive.


Part B) Is it possible for you to have driven 160 miles?


Please help and if you don’t mind to explain how you got all of the answers to each part. Offering 20 Points!

Thank you!

Respuesta :

JeanaShupp

Answer: A)[tex]t\leq3\\d\leq55t[/tex]

B) Yes

Step-by-step explanation:

Given:  Let 't' be the time in hours and 'd' be the distance( in hours ) traveled in t time.

Then the speed of driving=[tex]\frac{d}{t}[/tex]

Since, At most, we  are allowed to drive for three hours.

[tex]\Rightarrow\ t\leq3[/tex]...........(1)

Also, While driving, our maximum speed is 55 miles per hour.

[tex]\Rightarrow\ \frac{d}{t}\leq55\\\Rightarrow\ d\leq55t[/tex]

From (1), maximum time of driving is 3 hours

[tex]d\leq55(3)\\\Rightarrow\ d\leq165[/tex]

Thus, we can travel maximum distance 165 miles with this speed.

hence, it is possible to have driven 160 miles. (∵160<165)


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