Use a system of equations to solve the following problem A p

Use a system of equations to solve the following problem. A private jet flies the same distance in 7 hours that a commercial jet flies in 4 hours. If the speed of the commercial jet was 57 mph less than 2 times the speed of the private jet, find the speed of each jet.

Speed of private jet =

Speed of commercial jet =

Solution

Let Speed of private jet = x mph

Speed of commercial jet = y mph

A private jet flies the same distance in 7 hours that a commercial jet flies in 4 hours

7x = 4y ; 7x -4y ----(1)

2x -57 = y ; 2x -y = 57 ----(2)

Solve equation 1 and 2 :

multiply equation 2 by -2 :

-8x +4y = -228

7x -4y =0

--------------(add)

-x = -228

x = 228

4y = 7x ; y = (7/4)*228 = 399 mph

Speed of private jet = 228 mph

Speed of commercial jet = 399 mph