Question 708476: Hello, I need help with a uniform motion problem. I have tried different solutions and it is not the answer my book is offering.
Problem:
A speeding car traveling at 80 mph passes a police officer. Ten seconds later, the police officer gives chase at a speed of 100 mph. How long, in minutes, does it take the police officer to catch up with the car.
Book Answer:
2/3 of a minute
My work:
Well I use the four box method. So it looks something like this
First time rate * time = distance
Speeding car 80 x+10 80(x+10)
Police Car 100 x 100x
80(x+10)=100x
80x+800=100x
800=20x
40=x Incorrect to the book answer
Second time rate * time = distance
Speeding car 80 x 80x
Police car 100 x-10 100(x-10)
80x=100(x-10)
80x=100x-1000
-20x=-1000
x=50 Incorrect to the book answer
Then calculate for the police car by subtracting 10 gives you 40
This left me thinking if it is to the book answer maybe I need to use .1 instead of 10 because it is 10 seconds not minutes.
Third time rate * time = distance
Speeding car 80 x+.1 80(x+.1)
Police car 100 x 100x
80(x+.1)=100x
80x+8=100x
8=20x
8/20=x Then reduce by 4
2/5=x Again incorrect according to the book answer
So just to try it I flipped it again.
Fourth time rate * time = distance
Speeding car 80 x 80x
Police car 100 x-.1 100(x-.1)
80x=100(x-.1)
80x=100x-10
-20x=-10
x= 10/20
x=1/2 Then substitute 1/2-.1 or 1/2-1/10 = 5/10-1/10=4/10 reduce
x-.1=2/5 still an incorrect answer.
Answer by solver91311(24713)   (Show Source):
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