Two planes started at the same time from the same airport and flew in opposite directions... HELP!!!?

Question

Two planes started at the same time from the same airport and flew in opposite directions. One flew 60 miles per hour faster than the other. In 5 hours, they were 5,300 miles apart. Find the rate of each plane. Can somebody please explain to me how to solve these kind of questions?

Answer 1

let F = rate of faster plane
S = rate of slower plane
5300 = 5 S + 5 F . . . . equation 1
F = 60 + S . . . equation 2 . .. substitute to equation 1
5300 = 5 S + 5 (60 +S)
5300 = 5 S + 300 + 5S
10 S =5000
S = 500 mi/hr
F = 560 mi/hr

Answer 2

We will use the formula d = rt

Plane 1 Let x = rate of Plane 1
Plane 1 has traveled 5 hrs
Plane 1 distance = 5(x)

Plane 2 rate = x + 60 because one plane flew 60 mph faster Plane 2 has traveled 5 hrs
Plane 2 distance = 5(x + 60)

Okay, I always use a table to relate the data. We know that the planes are 5,300 miles apart, so if we add the distances of each plane together, we should get 5,300 miles. So, we just need to determine the distance of each plane. Thus, we use the formula d = rt (distance = rate * time). Since we only know one plane is going 60 mph faster than the other, we let x = the speed of one of the planes. That means the other planes speed will be x + 60. The problem tells us that the planes have been traveling 5 hours, so we will use that for the time of each plane, because they left at the same time and have been traveling the same amount of time. We then take the rate and time of each plane and multiply them together to get the distance.

Setting the problem up.

Distance of Plane 1 + Distance of Plane 2 = 5300
5x + 5(x + 60) = 5300
5x + 5x + 300 = 5300 Distribute
10x + 300 = 5300 Combine like terms
10x = 5000 Subtract 300
x = 500 Divide 10

Since x = 500, Plane 1 was going 500 mph
Plane 2’s rate = x + 60 = 500 + 60 = 560 mph

Answer 3

The basic formula for this type of problem is:

distance = speed x time
Let x = speed of the slower plane
Therefore, x + 60 = speed of faster plane
distance = 5,300 miles (given)
time = 5 hours

Solution:
distance of faster plane + distance of
slower plane = total distance between the
planes
(x)(5) + (x + 60)(5) = 5,300
5x + 5x + 300 = 5,300
10x + 300 = 5,300
10x = 5,300 - 300
10x = 5,000
x = 5,000/10
x = 500 miles per hour
500 + 60 = 560 miles per hour

Answers: 500 mi/hr = rate of slower plane
560 mi/hr = rate of faster plane.

That's it!
Hope I help you.

Teddy Boy

Answer 4

use the formula distance = speed x duration

let x be the speed of the slower plane

5x + 5(x+60) = 5300
5x + 5x + 300 = 5300
10x = 5000
x = 500

the speed (rate) = 500 and 560

Answer 5

use the rt = d formulation to paintings this situation. enable r = cost of the slower airplane. r + 40 = cost of the quicker airplane 5 hours = time the planes fly 2000 = entire distance for the two planes. 5r = distance of the slower airplane 5(r + 40) = distance the quicker airplane 5r + 5(r + 40) = 2000 5r + 5r + 2 hundred = 2000 10r + 2 hundred = 2000 10r = 1800 r = one hundred eighty mph