Plane speed question

Question

Two planes leave and airport at the same time, one flying east, the other flying west, the eastbound plane travels 110 mph slower. They are 2430 mi apart after 3 hr. What are the speeds of each plane?

Answer 1

Let x equal the speed in MPH of the plane flying West and (x-110) equal the speed in MPH of the plane flying East.

 

The distance between the planes after 3 hours is 2,430 miles.

Set up the Equation: Speed x Time = Distance

(3 hours)(x) + (3 hours)(x – 110) = 2430

3x + 3x – 330 = 2430

6x – 330 = 2430

Solve for speed: Distance/Time

6x = 2760

x = 460 MPH

Speed of plane traveling West: 460 MPH

Speed of plane traveling East: 460 – 110 = 350 MPH

Check: 460 * 3 = 1,380 miles

Check: 350 *3 = 1,050 miles

Check 1,380 + 1,050 = 2,430 miles

Answer 2

Let the planes be A and B.

Plane A flies East.

Plane B flies west.

 

If plane B flies at X miles per hour, it means Plane A flies at (X-110)miles per hour (because the eastbound plane is flying slower).

 

In 3 hours, the planes are 2430 miles apart.

 

Now, planes A and B are flying away from each other so in 3 hours, the distance between them is 2430miles measured in a straight line. 

 

So Distance = Speed x Time

 

For Plane A, Distance = (X-110) x 3 = 3X - 330. 

 

For Plane B, Distance = X times 3 = 3X

 

Total distance between these 2 planes = 2430

This means 3X - 330  PLUS 3X = 2430

(3X - 330) + 3X = 2430

 

6X - 330 = 2430

 

6X = 2430 + 330 = 2760

 

X = 460 miles per hour. This is Plane B's speed.

 

Plane A's speed would be 460 - 110 = 350 miles per hour. 

Answer 3

distance=rate*time

2430=r*3+(r-110)*3

2430=3r+3r-330

2430+330=6r

2760=6r

r=2760/6

r=460 mph

r-110=350 mph