A storm is approaching from the SW at 30 mph and is 7.5 miles away. An officer is 5 miles from the storm and needs to arrive 5 minutes ahead of the storm. How fast does he need to drive to reach the storm 5 minutes ahead?
figure out how much time it takes for the storm to arrive. Subtract five minutes. Now you have the time for the officer to travel, and you know his distance, so figure speed.
time taken for the storm to arrive = 7.5/30 hrs = .25 hrs = 15 minutes
So the officer must do his 5 miles in 10 minutes to arrive 5 min ahead of the storm
speed = dist./time = 5/(10/60) = 30 mph
To determine how fast the officer needs to drive, we can first calculate the time it will take for the storm to reach the officer's location.
Since the storm is 7.5 miles away and approaching at a speed of 30 mph, we can use the formula: time = distance / speed.
Calculating the time it will take for the storm to reach the officer's location:
time = 7.5 miles / 30 mph = 0.25 hours
Since the officer needs to arrive 5 minutes ahead of the storm, we need to convert 5 minutes to hours. We know that 1 hour is equal to 60 minutes, so 5 minutes is equal to 5/60 = 0.0833 hours.
So, to reach the storm 5 minutes ahead, the officer needs to drive at a speed that allows him to cover a distance of 5 miles in 0.0833 hours.
Calculating the required speed:
speed = distance / time = 5 miles / 0.0833 hours
To get the speed in miles per hour, we can divide the distance by the time. Therefore, the officer needs to drive at a speed of approximately:
speed = 5 miles / 0.0833 hours ≈ 60 mph
Therefore, the officer needs to drive at approximately 60 mph to reach the storm 5 minutes ahead.