1. a plane flew 800 miles in 4 hours with the wind. it
took 5 hours to travel the same distance against the
wind. what is the rate of the plane in still air and the
rate of the wind?
a plane: 190 mph; wind: 30 mph
b) plane: 180 mph; wind: 20 mph
plane: 200 mph; wind: 160 mph
d) plane: 190 mph; wind: 20 mph
c) plane: 190 mph; wind: 20

Option B

The rate of the plane in still air and the  rate of the wind is 180 miles per hour and 20 miles per hour respectively

Solution:

Given that, A plane flew 800 miles in 4 hours with the wind.  

It took 5 hours to travel the same distance against the wind.

We have to find what is the rate of the plane in still air and the rate of the wind?  

Let the speed of plane in still air be m and speed of wind be n.

Now, we know that, distance = speed x time.

Then, while travelling with wind ⇒ 800 = ( m + n ) x 4 ⇒ m + n = 200 ⇒ (1)

And, while travelling against wind ⇒ 800 = ( m – n ) x 5 ⇒ m – n = 160 ⇒ (2)

Now, solve the equations (1) and (2)

(1) ⇒ m + n = 200

(2) ⇒m – n = 160

(+) 2m + 0 = 360

2m = 360

m = 180

Now, substitute the m value in (1)

180 + n = 200 ⇒ n = 200 – 180 ⇒ n = 20

Hence, the speed of plane in still air is 180 miles per hour and speed of wind is 20 miles per hour.  Thus option B is correct

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

john earns $14.00 for two hours of work.