3.Sam is a mailman who delivers mail in a mail truck. His route is 2 kilometers long. He usually starts his route at 8:00 am and finishes by 12:00pm If Sam decided to get a bigger route that is 12 kilometers long, what does his average speed need to be to start and finish at his usual times?
Now wait a minute, try this yourself.
To find Sam's required average speed to complete a 12-kilometer route in the same time frame, we can use the formula:
Average Speed = Total Distance / Total Time.
1. Firstly, let's calculate the total time Sam usually takes to complete the 2-kilometer route. If he starts at 8:00 am and finishes at 12:00 pm, his total time is 4 hours.
2. To find Sam's average speed for the 2-kilometer route, divide the total distance by the total time:
Average Speed = 2 km / 4 hours = 0.5 km/h.
3. Now, we need to find the time it would take Sam to complete the 12-kilometer route at this average speed. Rearranging the formula, we can isolate total time:
Total Time = Total Distance / Average Speed.
Total Time = 12 km / 0.5 km/h = 24 hours.
4. Since Sam wants to finish his route by 12:00 pm (which is timespan of 4 hours), we need to determine how much time he has to complete the 12-kilometer route. We subtract the usual 4-hour timeframe from the 24-hour total time:
Extra Time = 24 hours - 4 hours = 20 hours.
5. Now, we can calculate the required average speed for Sam to complete the 12-kilometer route in 20 hours:
Average Speed = Total Distance / Total Time.
Average Speed = 12 km / 20 hours = 0.6 km/h.
Therefore, for Sam to start and finish a 12-kilometer route within his usual timeframe of 8:00 am to 12:00 pm, his average speed needs to be 0.6 km/h.