Distance rate and time

Question

two planes leave an airport at the same time, one flying east, the other flying west. The eastbound plane travels 60 mph slower. They are 3440 miles part after 4 hours. Find the speed of each plane. 

Answer 1

Since the East bound plane is going 60 miles slower, in 4 hours it would go 4x60 = 240 miles less than the Wsat bound plane. Thus if you add 240 miles to 3440 miles = 3680 miles that is what both the planes would have gone if both were going at the same speed ie the speed of the West bound plane. 

 

If you divide 3680 / 2 = 1840 miles that is what the West bound plane have gone in 4 hours.

Thus the speed of the West bound plane is 1840/4 = 460 mph

 

And the speed of the East bound plane was 400 mph

 

Check the total 460 x 4 + 400 x 4 = 3440 miles.

 

Have fun.

 

 

BTW I am also available for formal lessons online if you nay any more help.

 

 

Answer 2

Hi Raquel,

 

Time = 4 hours

 

If the distance that the east plane traveled is D, then the west plane traveled 3440 - D.

 

If the speed of the west plane is S, then the speed of the east plane is S - 60

 

Now plug into the equation, Distance = Speed x Time

 

East Plane:  D = (S-60) x 4 --> D = 4S - 240

 

West Plane: 3440 - D = S x 4--> Divide both sides by 4--> (3440-D)/4 = S

 

Substitute for S in the first equation--> D = 4 x (3440-D)/4 - 240

 

D = 3440 - D - 240

 

2D = 3200

 

D = 1600 miles = distance traveled by the east plane.

 

Now you can figure the distance of the west plane and then the planes' speeds by plugging back into the equations.

 

Have fun.

 

Dan

 

 

Answer 3

Distance = rate times time.

 

Let v be the speed of the faster (westbound) plane.  Let v - 60 be the speed of the eastbound plane.

 

How far has the faster plane gone in 4 hours?

 

d_fast = v(4)

 

 

How far has the slower plane gone in 4 hours?

 

d_slow = (v - 60)(4)

 

 

The sum of the two distances in 3440 miles.

 

4v + 4(v - 60) = 3440

 

Simplify.

 

4v + 4v - 240 = 3440

 

5v - 240 = 3440

 

5v = 3200

 

v = 640.

 

What is v, again?  The speed of the faster plane.

 

The westbound plane is going 640 mph.

 

The eastbound plane is going 580 mph.