Brian is trying to qualify for a race. A driver needs to complete 9 laps of a seven-mile track at an average speed of 114.78 mph to qualify. Brian has already completed the first three laps. His average speed so far is ninety-two mph. Approximately how many seconds will Brian need to finish the race to qualify?
To complete 9 laps of a seven-mile track, Brian needs to cover a distance of 63 miles (9 laps x 7 miles/lap).
To qualify, he needs to do this at an average speed of 114.78 mph.
So, the total time he needs to complete the race is:
63 miles ÷ 114.78 mph = 0.549 hours
To find the time needed to complete the remaining 6 laps (since he has already completed 3), we can subtract the time he has already taken from the total time needed:
Total time needed - Time taken = Time needed to complete remaining laps
0.549 hours - (3 laps ÷ 92 mph) = Time needed to complete remaining laps
0.549 hours - 0.03261 hours = 0.51639 hours
Converting this to seconds:
0.51639 hours x 3600 seconds/hour = 1858.004 seconds
Therefore, approximately 1858 seconds (or about 31 minutes) will be needed for Brian to finish the race and qualify.
To find out approximately how many seconds Brian will need to finish the race and qualify, we can follow these steps:
Step 1: Calculate the remaining distance to be covered.
Since Brian needs to complete a total of 9 laps, and he has already completed 3 laps, he has 9 - 3 = 6 laps remaining.
The track length is seven miles per lap, so the remaining distance is 6 laps * 7 miles/lap = 42 miles.
Step 2: Convert the remaining distance to feet.
Since 1 mile is equal to 5,280 feet, the remaining distance is 42 miles * 5,280 feet/mile = 221,760 feet.
Step 3: Calculate the remaining time Brian needs to finish the race.
Brian's average speed is given as 92 mph. To calculate the time needed in hours to finish the race, we can use the formula: Time = Distance / Speed.
So, the remaining time in hours is 221,760 feet / (92 mph * 5280 ft/mile) = 0.051 hours.
Step 4: Convert the remaining time to seconds.
Since there are 60 minutes in an hour and 60 seconds in a minute, the remaining time is 0.051 hours * 60 minutes/hour * 60 seconds/minute = 183.6 seconds.
Therefore, approximately, Brian will need about 183.6 seconds to finish the race and qualify.