80(x+12) = 71x
Solve for x.
Solve for x.
First, we need to convert the 12 minutes of delay into hours. Since there are 60 minutes in an hour, divide 12 by 60:
12 minutes รท 60 = 0.2 hours
Now, let's define the variables:
- t = time it takes for the police to catch up with the robbers
We can set up equations for the distance traveled by each party using the formula: distance = speed ร time.
For the robbers:
distance = speed ร time
distance = 71 mph ร (t + 0.2 hours)
For the police:
distance = speed ร time
distance = 80 mph ร t
Now, we can equate these two distances since at the moment the police catch up with the robbers, they would have traveled the same distance:
71 mph ร (t + 0.2 hours) = 80 mph ร t
Solving for t, we can simplify the equation:
71t + 14.2 = 80t
Rearranging the equation:
9t = 14.2
Dividing both sides by 9:
t = 14.2 รท 9
Simplifying, we find:
t โ 1.578 hours
Therefore, it will take approximately 1.578 hours for the police to overtake the robbers after the robbery.