If a plane can travel 470 miles per hour with the wind and 390 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
Let's assume the speed of the plane in still air is "p" and the speed of the wind is "w".
With the wind, the effective speed of the plane is increased by the speed of the wind. So, the speed of the plane with the wind is "p + w".
Against the wind, the effective speed of the plane is decreased by the speed of the wind. So, the speed of the plane against the wind is "p - w".
Given that the speed of the plane with the wind is 470 miles per hour and the speed of the plane against the wind is 390 miles per hour, we can set up the following equations:
p + w = 470 .......(1)
p - w = 390 .......(2)
Adding equations (1) and (2) will eliminate "w":
2p = 860
p = 430
Substituting the value of p into equation (1), we can solve for "w":
430 + w = 470
w = 470 - 430
w = 40
So, the speed of the plane in still air is 430 miles per hour, and the speed of the wind is 40 miles per hour.
You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $50.00 with a charge of $0.05 per minute for all long-distance calls. Plan B has a monthly fee of $15.00 with a charge of $0.15 per minute for all long-distance calls. Complete parts a and b.
a. For how many minutes of long-distance calls will the costs for the two plans be the same?
[ ] minutes
Let's denote the number of minutes of long-distance calls as "x".
For Plan A, the cost can be calculated as follows:
Cost of monthly fee + Cost per minute * Number of minutes
= $50 + $0.05 * x = 50 + 0.05x
For Plan B, the cost can be calculated as follows:
Cost of monthly fee + Cost per minute * Number of minutes
= $15 + $0.15 * x = 15 + 0.15x
To find the number of minutes of long-distance calls where the costs for the two plans are the same, we can equate the two expressions and solve for "x":
50 + 0.05x = 15 + 0.15x
Subtracting 0.05x and 15 from both sides:
35 = 0.1x
Dividing both sides by 0.1:
35/0.1 = x
x = 350
Therefore, for 350 minutes of long-distance calls, the costs for the two plans will be the same.
Part B) What will be the cost for each plan?
To find out the cost for each plan, we can substitute the value of "x" (number of minutes of long-distance calls) into the cost equations for Plan A and Plan B.
For Plan A:
Cost of monthly fee + Cost per minute * Number of minutes
= $50 + $0.05 * x = $50 + $0.05 * 350 = $50 + $17.50 = $67.50
So, the cost for Plan A with 350 minutes of long-distance calls would be $67.50.
For Plan B:
Cost of monthly fee + Cost per minute * Number of minutes
= $15 + $0.15 * x = $15 + $0.15 * 350 = $15 + $52.50 = $67.50
So, the cost for Plan B with 350 minutes of long-distance calls would also be $67.50.
Therefore, the cost for both plans would be $67.50 with 350 minutes of long-distance calls.
Part C) If you make approximately 15 long-distance calls per month, each averaging 20 minutes, which plan should you select?
To determine which plan would be more cost-effective given your usage of 15 long-distance calls per month, each averaging 20 minutes, we can compare the total costs for both plans.
For Plan A:
Cost of monthly fee + Cost per minute * Number of minutes
= $50 + $0.05 * (15 * 20) = $50 + $0.05 * 300 = $50 + $15 = $65
For Plan B:
Cost of monthly fee + Cost per minute * Number of minutes
= $15 + $0.15 * (15 * 20) = $15 + $0.15 * 300 = $15 + $45 = $60
Therefore, if you make approximately 15 long-distance calls per month, each averaging 20 minutes, selecting Plan B would be more cost-effective as it would cost $60, compared to $65 for Plan A.