You want to go on a road trip this weekend from Washington DC to Boston to visit your brother. You want to travel on Interstate 95, which is 438 miles long.
a. You are able to maintain an average speed of 60 mph. How long will the trip take you?
)b. You have been saving $25 a week to make the trip; you now have $200. This money will be budgeted to include gas, food, and entertainment. Write an equation to model your savings plan and then graph it. What would be the domain and range in this situation?
Your car will get 25 miles per gallon, and the average cost for gas along this route is $3.60 per gallon. You plan to take your brother on a tour of Boston and to dinner. The tour costs $34.99 per person for an 80-minute tour, and dinner is $17.50 per person. You have also calculated that other meals and snacks will cost $60.
c. How many gallons of gas will you need?
d. What is the cost of the gas?
e. How much will the tour and dinner cost for you and your brother?
f. Have you saved enough money to make the trip this weekend or do you need to wait? If you do need to wait, how many more weeks do you need to save enough money?
You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. You will have no access to any electricity, but you must be able to illuminate the entire grounds. You know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. Suppose the intensity is 90 when the distance is 5 m.
a. Write an equation to model the situation.
b. Solve for the constant of variation.
c. Write the equation to model the situation using the constant () of variation.
d. You have been given lanterns with 40 light intensity. Use your equation to solve for the distance from the lantern.
e. You need to illuminate 225 km. How many meters do you need to light?