Answer:
speed of one plane is 50 miles/hour
Speed of other plane is 82 miles/hour
Step-by-step explanation:
Given : Two airplanes leave the same place and fly in opposite directions. The average rate of one plane is 32 miles per hour faster than the other one.
To Find: . Find the rate of each plane if they are 1098 miles apart after 1 1/2 hours
Solution : Let the speed of one plane be x miles per hour
Time = ![1\frac{1}{2} =\frac{3}{2} =1.5 hours](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7B3%7D%7B2%7D%20%3D1.5%20hours)
So, distance traveled by one plane in 1.5 hours = speed * time
= 1.5 x
Since we are given that speed of other plane is 32 more than one
So, speed of other plane is x+32 miles per hour
Time = 1.5 hours
So, distance traveled by other plane in 1.5 hours = speed * time
= 1.5 (x+32)
Since they are 1098 miles apart after 1.5 hours
So, ![1.5x+1.5(x+32)=1098](https://tex.z-dn.net/?f=1.5x%2B1.5%28x%2B32%29%3D1098)
![1.5x+1.5x+48=1098](https://tex.z-dn.net/?f=1.5x%2B1.5x%2B48%3D1098)
![3x+48=1098](https://tex.z-dn.net/?f=3x%2B48%3D1098)
![3x=1050](https://tex.z-dn.net/?f=3x%3D1050)
![x=\frac{1050}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1050%7D%7B3%7D)
![x=50](https://tex.z-dn.net/?f=x%3D50)
So, speed of one plane is 50 miles/hour
Speed of other plane is x+32=50+32 =82 miles/hour