SOLUTION: You travel the first 48 miles of a journey at an average of 36 mph and the second 48 miles at an average of v mph. What must be v if you want to average 45 mph over the 96 mile jou

Question 1140236: You travel the first 48 miles of a journey at an average of 36 mph and the second 48 miles at an average of v mph. What must be v if you want to average 45 mph over the 96 mile journey?

Found 4 solutions by Alan3354, Theo, josgarithmetic, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
You travel the first 48 miles of a journey at an average of 36 mph and the second 48 miles at an average of v mph. What must be v if you want to average 45 mph over the 96 mile journey?
-------------
Avg speed of a round trip or of equal parts is:
Avg = 2*r1*r2/(r1 + r2)
----
45 = 2*36*r2/(36+r2)
45*(36+r2) = 72r2
1620 + 45r2 = 72r2
27r2 = 1620
r2 = 60 mi/hr
=====================================
IMO, this is a formula you should remember. It's similar to parallel work, parallel flow, parallel resistors, etc. Only the factor of 2 is different.
You can remember it, or not.
---
It's also the basis for the famous Michelson-Morley experiment that showed no effects of the "ether" and dispelled belief in the existence of the ether. Ether is now stored in the same closet as phlogiston.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
r * t = d

r = rate
t = time
d = distance.

for the first 48 miles, the equation becomes r1 * t1 = 48
for the second 48 miles, the equation becomes r2 * t2 = 48

since r1 = 36, the first equation becomes 36 * t1 = 48
solve for t1 to get t1 = 48/36

since r2 = v, the second equation becomes v * t2 = 48

for the overall trip, r * t = 96
r is the overall rate
t is the overall time

since r = 45, then r * t = 96 becomes 45 * t = 96.
solve for t to get t = 96/45

since t1 + t2 = t, you get 48/36 + t2 = 96/45
that makes t2 = 96/45 - 48/36 = .8

you now have:

r1 = 36
t1 = 48/36
r2 = v
t2 = .8

you know that r2 * t2 = 48 and you know that r2 = v and t2 = .8, so you get v * .8 = 48.
solve for v to get v = 48/.8 = 60

that's your solution.

you now have:

r1 = 36
t1 = 48/36
r2 = 60
t2 = .8

since r1 * t1 + r2 * t2 = r * t, the formula becomes:

36 * 48/36 + 60 * .8 = 45 * 96/45

simplify to get 48 + 48 = 96 which is true, confirming the solution is correct.

Answer by josgarithmetic(39631)   (Show Source): You can put this solution on YOUR website!
total time:

total distance:

EQUATION
-----solve for v.
-

Answer by ikleyn(52925)   (Show Source): You can put this solution on YOUR website!
.

1. "You travel the first 48 miles of a journey at an average of 36 mph". It means that you spent = hours = hours = 1 hour and 20 minutes for this part of the journey. 2. "you want to average 45 mph over the 96 mile journey". It means that you spend = hours = hours = hours = 2 hours and 8 minutes for the entire journey of 96 miles. 3. So, you have 2 hours 8 minutes - 1 hour 20 minutes = 128 minutes - 80 minutes = 48 minutes for the second part of 48 miles long. 4. Thus your speed on the seconf leg of 48 miles should be = 1 miles per minute or 60 miles per hour. ANSWER

Solved.

-----------------

You do not need use complicated formula.

You do not need use equations, at all.

To solve the problem, all you need is to apply your common sense.

RELATED QUESTIONS
“You travel the first 48 miles of a journey at an average of 36mph and the second... (answered by josgarithmetic)
A motorist travels 120 miles from Antwerp to Brussels at an average speed of 48 mph. She... (answered by ReadingBoosters)
Hailee drove to a park 48 miles away at an average speed of 53 mph. What is the total... (answered by Alan3354)
You drive 100 miles. Over the first 50 miles you drive 50 mph, and over the second 50... (answered by ewatrrr)
A man drove the first 75 miles of a trip at an average of 50mph. He then drove the next... (answered by ankor@dixie-net.com)
A motorist travels 120 miles from Antwerp to Brussels at an average of 40 mph. She... (answered by Alan3354)
Travis made a business trip of 128 miles. He averaged 56 mph for the first part of the... (answered by TimothyLamb)
Joe left Southlake on his bicycle riding at an average rate of 8 miles per hour...five... (answered by ankor@dixie-net.com)
a trunk travels 150 miles on the freeway at an average speed of 60 mph. how long does the (answered by hamsanash1981@gmail.com)