SOLUTION: Some bank robbers leave town, speeding at 70 mph. Ten minutes later, the police give chase, traveling at 78 mph. How long will it take the police to overtake the robbers?
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Question 107492This question is from textbook College Algebra
: Some bank robbers leave town, speeding at 70 mph. Ten minutes later, the police give chase, traveling at 78 mph. How long will it take the police to overtake the robbers? This question is from textbook College Algebra
You can put this solution on YOUR website! Some bank robbers leave town, speeding at 70 mph. Ten minutes later, the police give chase, traveling at 78 mph. How long will it take the police to overtake the robbers?
:
Let t = travel time of the cops
The crooks had a 10 min head start, change 10 min to hrs: 10/60 = 1/6 hr
(t + (1/6)) = travel time of the crooks
:
We know when the cops overtake the crooks they will have traveled the same distance,
Write a distance equation from this fact: Distance = speed * time
:
78t = 70(t + )
:
78t = 70t +
:
78t - 70t =
:
8t =
:
Multiply equation by 6 to get rid of the denominator, you then have:
48t = 70
:
t =
:
t = 1.4583 hrs, or 1 hr 27.5 min
:
Check our solution with a calc by finding that the distances are the same:
Cops: 78 * 1.4583 = 113.75 miles
Crooks: 70 * (1.4583 + (1/6)) = 113.5 miles also
You can put this solution on YOUR website! 10 minutes is hour, so in the first 10 minutes, the robbers will have traveled miles, or miles. Since the police are travelling 8 mph faster than the robbers, the question becomes how long will it take to travel 11 and 2-thirds miles at 8 mph.
hour.
To check, realize that the robbers have been travelling for 10 minutes (0.167 hour) longer than the police, so the robbers have been travelling 1.46 + 0.167 = 1.63 hours
. They are the same, so 'You are under arrest, you have the right...'
