a private jet flies the same distance in 6 hours that a commercial jet flies in 4 hours.if the speed of the commercial jet was 143 mph less than 2 times the speed of the private jet, find the speed of each jet
To solve this problem, we need to set up equations using the given information and then solve them simultaneously.
Let's denote the speed of the private jet as P mph and the speed of the commercial jet as C mph.
According to the given information, the private jet flies the same distance in 6 hours as the commercial jet flies in 4 hours. This can be expressed as:
Distance traveled by private jet = Distance traveled by commercial jet
P x 6 = C x 4
Now, we are also told that the speed of the commercial jet is 143 mph less than 2 times the speed of the private jet. This can be expressed as:
C = 2P - 143
Now we have a system of two equations:
P x 6 = C x 4 ...(Equation 1)
C = 2P - 143 ...(Equation 2)
To solve this system of equations, we can substitute the value of C from Equation 2 into Equation 1:
P x 6 = (2P - 143) x 4
Simplifying this equation:
6P = 8P - 572
-2P = -572
Dividing both sides by -2:
P = 286
Now that we have the value of P, we can substitute it back into Equation 2 to find the value of C:
C = 2P - 143
C = 2(286) - 143
C = 572 - 143
C = 429
Therefore, the speed of the private jet is 286 mph, and the speed of the commercial jet is 429 mph.
speed of private jet --- x mph
speed of commercial jet --- 2x-143 mph
They both went the same distance, so ...
4(2x - 143) = 6x
solve for x