A person travel 1600 miles by commercial jet then an additio

A person travel 1600 miles by commercial jet, then an additional 500 miles by private plane. If the speed of the jet is 4 times the speed of the private plane, and total time in the air was 6 hours, determine the speed of each plane.
I have tried the problem as: 4x/1600 + x/500 = 6, and also 1600/4x = 500/x - 6 , and a few other variations on this, but can\'t seem to come up with the correct answer, which the book has as 150 mph, and 600 mph. I\'m think I\'m close, but can\'t figure out what I\'m doing wrong

Solution

Private plane is travelling at v mph
Jet is travelling at 4v mph
Time on jet is 1600/4v and time on private plane is 500/v
Total time is 6 = 1600/4v + 500/v
Multiply by 4v throughout and get
24v = 1600 + 2000 so
24v = 3600
v = 150
So Private plane travels at 150 mph and jet at 600
1600/600 = 2 2/3 hours
500/150 = 3 1/3 hours
Total = 6 hours