You allow yourself 34 min to drive 26 mi to the airport, but you're caught in heavy traffic and average only 15 mi/h for the first 13 min . What must your average speed be on the rest of the trip if you're to make your flight?
you went 15/60 * 13 = 3.25 miles in first 13 min
so
26 - 3.25 = 22.75 miles left
and
34 - 13 = 21 minutes left which is 21/60 = .35 hours
so
22.75 miles/.35 hours = 65 mph
Well, in this situation you need to become the Usain Bolt of driving! To calculate your required average speed for the rest of the trip, let's do some clown math. You originally allotted yourself 34 minutes to travel 26 miles. However, you were only able to cover 15 miles in the first 13 minutes. That means you have 21 minutes left for the remaining 11 miles of your trip.
So, to make sure you catch your flight, you'll need to channel your inner racecar driver and maintain an average speed of approximately 31.4 miles per hour (11 miles divided by 21 minutes). Just make sure you don't get pulled over for clownish driving maneuvers!
To find out what your average speed must be for the rest of the trip, we need to first calculate the distance you have already traveled in the first 13 minutes.
Distance = Rate * Time
Given that your average speed in the first 13 minutes is 15 mi/h, and the time is 13 minutes, we can calculate:
Distance = 15 mi/h * (13 min / 60 min/h)
Distance ≈ 15 mi/h * 0.22 h ≈ 3.3 miles
Now, we need to find the remaining distance to the airport:
Remaining distance = Total distance - Distance traveled in the first 13 minutes
Remaining distance = 26 miles - 3.3 miles ≈ 22.7 miles
Now, let's calculate the time you have left to cover the remaining distance:
Time left = Total time - Time already spent
Time left = 34 min - 13 min ≈ 21 min
Finally, to find your average speed for the remaining distance, we can use the formula:
Average speed = Remaining distance / Time left
Average speed = 22.7 miles / (21 min / 60 min/h)
Average speed ≈ 22.7 miles / 0.35 h ≈ 64.9 mi/h
Therefore, to make your flight, you would need to average approximately 64.9 miles per hour for the rest of the trip.
To determine the average speed you need for the rest of the trip, let's calculate how much time you have left after the first 13 minutes.
Given:
Total time allowed: 34 minutes
Time spent in heavy traffic: 13 minutes
Time remaining: 34 minutes - 13 minutes = 21 minutes
Next, let's calculate how much distance you have left to cover after the first 13 minutes.
Given:
Total distance to the airport: 26 miles
Distance covered in heavy traffic: 15 miles
Distance remaining: 26 miles - 15 miles = 11 miles
Now, to calculate the average speed you need for the rest of the trip, you can use the formula:
Average speed = Distance / Time
Average speed = 11 miles / 21 minutes
To convert the time from minutes to hours, you divide by 60.
Average speed = 11 miles / (21 minutes / 60 minutes per hour)
Simplifying, we get:
Average speed = 11 miles / (21/60) hours
Average speed = 11 miles / (21/60) hours * (60/60)
Average speed = 11 miles / (21/60) hours * (60/60) * (1 mile/1 mile)
Average speed = 11 miles * (60/21) miles per hour
Simplifying further, we get:
Average speed = 31.43 miles per hour
Therefore, you must maintain an average speed of approximately 31.43 miles per hour for the remainder of the trip to make your flight.