Question

a plane can fly 1040 miles in the same time as it takes a car to go 320 miles. if the car travels 90 mph slower than the plane, find the speed of the plane.
a) using the variable ( x ) to represent the rate at which the plane flies, write an equation using the information as it is given above that can be solve this problem.
equation:

b) the speed of the plane is mph
question help: video message instructor

Explanation:

Part A

Step1: Recall time formula

Time \( t \) is given by \( t=\frac{\text{distance}}{\text{speed}} \). Let the speed of the plane be \( x \) mph. Then the speed of the car is \( (x - 90) \) mph.

Step2: Time for plane and car

Time taken by plane to fly 1040 miles: \( \frac{1040}{x} \). Time taken by car to go 320 miles: \( \frac{320}{x - 90} \).

Step3: Set times equal

Since their times are equal, the equation is \( \frac{1040}{x}=\frac{320}{x - 90} \).

Step1: Cross - multiply the equation

From \( \frac{1040}{x}=\frac{320}{x - 90} \), cross - multiply: \( 1040(x - 90)=320x \).

Step2: Expand the left - hand side

\( 1040x-93600 = 320x \).

Step3: Subtract \( 320x \) from both sides

\( 1040x-320x-93600=320x - 320x \), which gives \( 720x-93600 = 0 \).

Step4: Add 93600 to both sides

\( 720x=93600 \).

Step5: Solve for \( x \)

Divide both sides by 720: \( x=\frac{93600}{720}=130 \).

Answer:

\( \frac{1040}{x}=\frac{320}{x - 90} \)

Part B