A military jet flies directly over and at a right angles to the straight line course of a commercial jet. The military jet is flying 200 mph faster than four times the commercial jet. How fast is each going if they are 2050 miles apart (on a straight line) after one hour?
C=speed of commercial jet in mph
M=speed of military jet
=4C+200 mph
Distance after one hour, using Pythagoras theorem
=√(C²+M²)=2050
Solve for C and M
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the speed of the commercial jet is "x" mph. According to the problem, the military jet is flying 200 mph faster than four times the speed of the commercial jet, so its speed can be expressed as "4x + 200" mph.
Now, we know that both jets have been flying for one hour, and they are 2050 miles apart. The total distance covered by both jets can be calculated using the formula: Distance = Speed × Time.
For the commercial jet:
Distance = Speed × Time
Distance = x mph × 1 hour
Distance = x mph
For the military jet:
Distance = Speed × Time
Distance = (4x + 200) mph × 1 hour
Distance = (4x + 200) mph
Now, we can write the equation based on the given information:
Distance covered by the commercial jet + Distance covered by the military jet = Total distance apart
x mph + (4x + 200) mph = 2050 miles
Simplifying the equation:
5x + 200 = 2050
5x = 2050 - 200
5x = 1850
Dividing both sides by 5:
x = 1850 / 5
x = 370
Therefore, the speed of the commercial jet is 370 mph, and the speed of the military jet is 4x + 200:
Speed of the military jet = 4(370) + 200
Speed of the military jet = 1480 + 200
Speed of the military jet = 1680 mph
So, the commercial jet is flying at 370 mph, and the military jet is flying at 1680 mph to be 2050 miles apart after one hour.