SOLUTION: The sum of the digits of a certain two-digit number is 8. Reversing its digits decreases the number by 36. What is the number? A plane traveled 720 miles to Tokyo and back. The

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Question 977943: The sum of the digits of a certain two-digit number is 8. Reversing its digits decreases the number by 36. What is the number?
A plane traveled 720 miles to Tokyo and back. The trip there was with the wind. It took 6 hours. The trip back was into the wind. The trip back took 12 hours. Find the speed of the plane in still air and the speed of the wind.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
x is the tens digit
y is the ones digit
10x+y is the number and 10y+x is the reverse
10x+y-36=10y+x
9x-36=9y
9x=9y+36
x=y+4
x+y=8
y+4+y=8 by substitution
2y=4
y=2
x=6
62-36=26
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120 mph average on the way there, which is x+y
60 mph average on the way back, which is x-y
x+y=120
x-y=60
2x=180
x=90 mph of plane in still air
y=30 mph of wind