Final answer:
The speed of the private jet is 68.8 mph and the speed of the commercial jet is 34.4 mph.
Step-by-step explanation:
Let's assume the speed of the private jet is x mph.
According to the information given, the private jet flies the same distance in 8 hours that the commercial jet flies in 4 hours.
So, the speed of the private jet is: Distance / Time or x = Distance / 8.
Next, we are told that the speed of the commercial jet is 172 mph less than 3 times the speed of the private jet, which can be represented as: 3x - 172 = Speed of the commercial jet.
Now, we can set up an equation using the information above. Since the distance traveled is the same for both jets, we can equate the two expressions for distance:
x/8 = (3x - 172)/4
To solve for x, we can cross-multiply and simplify:
4x = 8(3x - 172)
4x = 24x - 1376
1376 = 24x - 4x
20x = 1376
x = 68.8
So, the speed of the private jet is 68.8 mph and the speed of the commercial jet is 3(68.8) - 172 = 34.4 mph.