SOLUTION: A plan flew from Boston to Paris at an average speed of 550 mph. On the return trip the plan flew at an average speed of 650 mph. Your friend claimed that the average speed for the

Algebra ->  Expressions-with-variables -> SOLUTION: A plan flew from Boston to Paris at an average speed of 550 mph. On the return trip the plan flew at an average speed of 650 mph. Your friend claimed that the average speed for the      Log On


   

Question 274384: A plan flew from Boston to Paris at an average speed of 550 mph. On the return trip the plan flew at an average speed of 650 mph. Your friend claimed that the average speed for the round trip was 600 mph. Do you agree or disagree with your friend’s claim? If you agree, Please provide a supporting argument. If you do not agree, please show a convincing argument to support your answer.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A plan flew from Boston to Paris at an average speed of 550 mph.
On the return trip the plan flew at an average speed of 650 mph.
Your friend claimed that the average speed for the round trip was 600 mph.
Do you agree or disagree?
:
Disagree,
Let d = dist from B to P
Let a = average speed
:
Write a time equation: Time = dist/speed
:
B/P time + P/B time = round-trip time
d%2F550 + d%2F650 = %282d%29%2Fa
divide by d:
1%2F550 + 1%2F650 = 2%2Fa
Multiply by 357500a (550*650), results:
650a + 550a = 2(357500)
:
1200a = 715000
a = 715000%2F1200
a = 595.8 mph is the average speed
:
:
Confirm this by finding the times, use 3000 miles
3000/550 = 5.45 hrs
3000/650 = 4.62 hrs
-------------------
total time 10.07 hrs
:
Using average speed for 6000 mi
6000/595.8 = 10.07 hrs