some bank robbers leave town traveling at 70 mph. Ten minutes later, the police are chasing them at 78mph. How long will it take the police to overtake the robbers.
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10
To determine how long it will take for the police to overtake the robbers, we need to find the time it takes for the police to close the distance between them.
First, let's convert the ten minutes delay of the police into hours:
10 minutes = 10/60 = 1/6 hours
Now, we can calculate the head start distance of the robbers:
Head start distance = Speed × Time
= 70 mph × 1/6 hours
= 70/6 miles
Now, we can consider that both the robbers and the police are traveling towards each other, and the relative speed between them is:
Relative speed = Police speed - Robbers speed
= 78 mph - 70 mph
= 8 mph
To calculate the time needed for the police to overtake the robbers, we can apply the formula:
Time = Distance / Relative speed
Time = (70/6 miles) / (8 mph)
= (70/6) / 8
= 70 / (6 * 8)
= 70 / 48
= 1.458 hours
To express time in minutes, we can convert it by multiplying by 60:
1.458 hours × 60 minutes/hour
= 87.5 minutes
Therefore, it will take approximately 87.5 minutes for the police to overtake the robbers.