SOLUTION: Could someone PLEASE help me with these? I need help badly. Thanks for your time. 1. A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Could someone PLEASE help me with these? I need help badly. Thanks for your time. 1. A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point       Log On


   

Question 31725: Could someone PLEASE help me with these? I need help badly. Thanks for your time.
1. A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane’s speed in still air?
2. Solve for x. 2/5=x-2/20
3. Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
1.
A total distance of 720 miles with x sppeed:
Equation:

Cross multiply

720[(x+30)+(x-30)]=10[(x+30)(x-30)]

1440x=10%28x%5E2-900%29

10x%5E2-1440x-9000

Divide the equation by 10:



Use the quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

a=1, b=-144, c=-900

x+=+%28-%28-144%29+%2B-+sqrt%28+%28-144%29%5E2-4%2A1%2A-900+%29%29%2F%282%2A1%29+

x=%28144%2B-sqrt%28+20736%2B3600%29%29%2F2

x=%28144%2B-sqrt%2824336%29%29%2F2 --->Remove the negative:

x=%28144%2B156%29%2F2

x=150

Hence, the speed of the plane is 150mph.



2.2%2F5=x-2%2F20

Multiply the whole equation by 20 and simplfy:

20%282%2F5%29=20%28x%2F1%29-20%282%2F20%29

4(2)=20(x)-2

10=20x

x=0.5



3.Simple intest is given by A=(prinicpal * Time * rate)/100 

Let the rate be x:



1500x=16500

x=11 (rate)

A=%282500%2A1%2A11%29%2F100

x=275

Hence, the rate is 11% and with he same rate the money earned is $275.

Paul.