write a system of inequalities

Question

During a family trip, you split the driving with your dad.At most, you are allowed to drive for 3 hours. While driving, your maximum speed is 55 miles per hour. Write a system of inequalities describing the possible numbers of hours (t) and distance (d) you may have to drive.

Answer 1

This is a d-i-r-t (Distance-Is-Rate-times-Time) problem.

 

d=rt

 

d is in miles

r is in miles per hour

t is in hours

 

"At most, you are allowed to drive for 3 hours"   means    t≤3

"your maximum speed is 55 miles per hour"    means r≤55

 

possible hours (t):     t≤3

possible distance (d):  d=rt

    t≤3

    rt≤r3     [multiply both sides by maximum +r and retain sense of inequality]

    rt≤(55)3

    rt≤165

    d≤165 miles   [you may drive no more than 165 miles]