SOLUTION: A bank robber holds up a bank and speeds away on the freeway at 80 miles per hour. Thirty minutes later, police officers, having gotten a description from people at the bank, take

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Question 320038: A bank robber holds up a bank and speeds away on the freeway at 80 miles per hour. Thirty minutes later, police officers, having gotten a description from people at the bank, take off in pursuit at 90 miles per hour. How long will the police have to drive to catch up, and how far from the bank will they catch the robber?
Found 3 solutions by mananth, Edwin McCravy, richwmiller:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
speed of robber = 80mph
speed of police = 90mph
robber has traveled 40 miles when the police start.( police start 1/2 hour later)
Let them meet at distance x from the bank.
time taken by police = x/90 hours
time taken by robber in the same time = x-40/80.
..
x/90 = x-40/80
80x=90(x-40)
80x = 90x-3600
10x=3600
x= 360 miles. The distance where they catch up with the robber from the bank.
''
speed of police = 90mph
distance = 360 miles
time they catch up = 360/90
= 4 hours

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
A bank robber holds up a bank and speeds away on the freeway at 80 miles per hour. Thirty minutes later, police officers, having gotten a description from people at the bank, take off in pursuit at 90 miles per hour. How long will the police have to drive to catch up, and how far from the bank will they catch the robber?

Make this chart

          DISTANCE       RATE       TIME
Robber
Police

Let the police's time be x. So fill in x for the Police's time.

          DISTANCE       RATE       TIME
Robber                
Police                                x

Fill in the two speeds:

          DISTANCE       RATE       TIME
Robber                    80 
Police                    90          x

The robber has a 30 minute headstart, so the robber's time is 
1%2F2 hour more than the police's time of x hours, so fill
in x+1%2F2 for the Robber's time:

          DISTANCE       RATE       TIME
Robber                    80         x+1%2F2
Police                    90          x
 
Now use DISTANCE = RATE × TIME to fill in the rest of the chart:

          DISTANCE       RATE       TIME
Robber     80(x+1%2F2)       80         x+1%2F2
Police       90x          90          x

The robbers and the police both went the same distance, so
we set the two distances equal:

80(x+1%2F2) = 90x
80x+40 = 90x
  -10x = -40
     x = 4

So it took the cops 4 hours to catch the crooks.

The distance was 90x or 90(4) or 360 miles.

Edwin

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
In 30 minutes the thief can go 40 miles.
The cops are going 10 mph faster than the thief.
It will take the cops 4 hours to go 40 miles at 10 mph
After 4 hours, the cops go 360 miles.