Your house, the library, your favorite coffee shop and the grocery store are all

Question

 Your house, the library, your favorite coffee shop and the grocery store are all on the same straight road, in a row, in that order. It is 1600 feet from your house to the library, 800 feet farther to the coffee shop and, 1900 feet farther to the grocery store. It may be helpful to sketch a picture. You have run out of data on your phone for the month, but you have access to the WiFi at each of these places as long as you are within 250 feet of the building. You are walking home from the grocery store at a constant rate of 2 miles per hour. 

(a) Write an equation for the distance in feet you are away from home as a function of the time, t, in minute. (Be careful of units, you may want to convert 2mph into feet per minute)

(b) Write a series of inequalities that describe the times at which you have access to WiFi if you continue this constant rate of travel. 

(c) Solve these inequalities and give the solution set. How much total time does it take you to get home from the grocery store, and how much of that are you able to access WiFi? 

(d) How fast must you travel if you can’t stand to be disconnected for more than 3 minutes? 

Explanation / Answer

a) 2 miles per hour = 176 feet/minute

Distance = Speed * Time

Distance from grocery store too house = 4300 feet

Distance covered per min = 176 feet

distance covered in time t = 176t

So, distance in feet you are away from home = 4300 - 176t

b) till 250 feet within grocery store i will have wifi access

So, 250/176 = 1.42 minute

That is from the star till 1.42 minute i will have wifi access

Then prior to 250 feet from coffee shop i will have access

so, i need to cover 1900-250-250 = 1400 feet more to have wifi access

Time = 1400/176 = 7.95 minutes to cover this distance

I will have access for 1.42 minutes each more before and after passing the coffee shop.

Then i will have to cover 800-250-250 = 300 feet to have wifi access again before library

i.e. 300/176 = 1.70 minutes no access

Then 1.42*2 minutes access before and after library

Then 1.42 minute before my house.

Inequalities:

x < 1.42

From 1.42<x<7.95 no access

then for 1.42*2 i will have access

So, total time of wifi access = 1.42 + 1.42*2 + 1.42*2 + 1.42 = For 8.52 minutes i will have wifi access

c) Total time to home = 4300/176 = 24.43 minutes out of which i can access wifi for 8.52 minutes

d) I should travel at:

Out of 4300 feet i will be connected 1500 feet with wifi

So, 2800 feet i will be disconnected no matter how fast i travel.

So, for discoonection time to be less than 3 minutes, i should travel at

2800/y < 3

or y > 933.33 feet per minute or 10.6 miles per hour

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.