1 Mr Huerta has 600 minutes per week to give individual help

1. Mr. Huerta has 600 minutes per week to give individual help to students. He averages 20 minutes per student. If he reduces the time per student by t minutes to (20 – t) minutes, he can meet with 600/(20-t) students. Write an inequality that describes each situation below and solves the inequality.

a. How many will fewer minutes per student allow Mr. Huerta to work with at least 36 students?

b. How many more minutes per student will allow Mr. Huerta to work with no more than 27 students?

2. The equation d=rt relates the distance d you travel., the time t takes to travel that distance and the rate r at which you travel.so the time takes is t =d/r.If you increase your rate ay a to r+a,then it takes less time t =d/r+a.In fact, the time you save by going at a faster rate is

T=(d/r)-(d/r+a)

a. You normally take a 500-mi trip, averaging 45 mi/h.You want to increase the rate so that your travel time is at least 1h shorter. write an inequality that describes the situation.

b. solve your inequality in part (a)

Solution

a) No. of students = 600/(20 -t)

Atleast 36 students : 36 < 600/(20 -t)

(20 - t) < 16.67

t > 3.33 min.

b) 27 >= 600/( 20 - t)

20- t > 22.22

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