Joseph traveled from Boston to Framingham at 50 mph and then back to Boston at 40 mph. What was Joseph's average speed on the round trip?
Key fact:
the distance is the same each way
time to go from B to F = d/50
time to go from F to B = d/40
avg speed = total distance/total time
= 2d/(d/50 + d/40)
= 2d/[(4d + 5d)/200]
= 2d * (200)/9d
= 400/9 or appr 44.4 mph
Joseph traveled from Boston to Framingham at 50 mph and then back to Boston at 40 mph. What was Joseph's average speed on the round trip?
Well, Joseph seems to be taking his sweet time! If you calculate the total distance he traveled, divide it by the total time he took, you'll get his average speed. So, what do you get when you combine the speed of a turtle with the speed of a snail? Joseph's average speed!
To calculate Joseph's average speed on the round trip, we need to find the total distance traveled and divide it by the total time taken. Here's how you can go about it:
Step 1: Determine the distance between Boston and Framingham.
Since we know the speed from Boston to Framingham is 50 mph, we need to find the actual distance between the two cities. Unfortunately, the question doesn't provide this information, so we cannot calculate the distance precisely without more details.
Step 2: Assume a value for the distance.
Since we don't have the exact distance, we can make an assumption or estimate. Let's assume the distance between Boston and Framingham is 40 miles for demonstration purposes. Remember that this is just an example assumption and not the actual value.
Step 3: Calculate the time taken for the outbound trip.
Using the assumed distance of 40 miles and the speed of 50 mph, we can calculate the time taken for the outbound trip (from Boston to Framingham). To find the time, we use the formula: time = distance / speed.
So, time = 40 miles / 50 mph = 0.8 hours (or 48 minutes).
Step 4: Calculate the time taken for the inbound trip.
Similarly, we need to find the time taken from Framingham back to Boston. The speed for this part of the trip is given as 40 mph. Using the assumed distance of 40 miles, we can calculate the time: time = distance / speed.
So, time = 40 miles / 40 mph = 1 hour.
Step 5: Calculate the total distance.
Since Joseph traveled the assumed distance of 40 miles from Boston to Framingham and then back to Boston, the total distance for the round trip would be 2 times the assumed distance.
Total distance = 2 * 40 miles = 80 miles.
Step 6: Calculate the total time taken.
Since Joseph spent 0.8 hours for the outbound trip and 1 hour for the inbound trip, the total time taken will simply be the sum of the two.
Total time = 0.8 hours + 1 hour = 1.8 hours (or 1 hour and 48 minutes).
Step 7: Calculate the average speed.
Finally, to find the average speed, we divide the total distance by the total time.
Average speed = Total distance / Total time.
So, average speed = 80 miles / 1.8 hours = approximately 44.4 mph.
Therefore, assuming the distance between Boston and Framingham is 40 miles, the average speed for Joseph's round trip would be approximately 44.4 mph.