Question 388672: A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hours and sees the same 2 digits in reverse order. 1 hours later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A person drives with constant speed and after some time he sees a milestone with 2 digits.
Then travels for 1 hour and sees the same 2 digits in reverse order.
1 hours later he sees that the milestone has the same 2 digits with a 0 between them.
What is the speed of the car?
:
Let x = the 1st digit on the first mile stone
Let y = the 2nd digit
:
Let s = speed of the car
:
"Then travels for 1 hour and sees the same 2 digits in reverse order."
10x + y + 1s = 10y + x
10x - x + s = 10y - y
9x + s = 9y
:
"1 hours later he sees that the milestone has the same 2 digits with a 0 between them."
10y + x + s = 100x + y
10y - y + s = 100x - x
9y + s = 99x
:
Rearrange the above two equations for elimination
9x - 9y + s = 0
-99x+9y + s = 0
----------------adding eliminates y
-90x + 2s = 0
2s = 90x
s = 45x
x has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added to
a two digit milestone, could not be at another two digit milestone.)
:
Find y
9x + s = 9y
9(1) + 45 = 9y
9 + 45 = 9y
simplify divide by 9
1 + 5 = y
y = 6
:
Speed is 45 mph, x=1, y=6; 1st mile marker 16
:
Try this:
1st milestone: 16
travel one hr +45
2nd milestone: 61
travel one hr:+45
3rd milestone:106
|
|
|
