SOLUTION: if a man walks a distance at 3 mph and jogs back the same route at 5 mph and the trip takes one hour how many miles did he travel

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Question 1134632: if a man walks a distance at 3 mph and jogs back the same route at 5 mph and the trip takes one hour how many miles did he travel
Found 4 solutions by mathsolverplus, ikleyn, Alan3354, greenestamps:
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = amount of hours spent
Distance is the same for both trips:
3t = 5(1-t)
3t = 5-5t
8t = 5
t = 5/8 hr
Distance traveled in total:
2(3t) = 30/8 = 15/4 miles
OR
3t + 5(1-t) = 3(5/8) + 5(3/8) = 15/8 + 15/8 = 15/4 miles



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Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

There is ANOTHER way to solve the problem, and it's worth to know it. 

Let  d  be one way distance.


Then the time to go "there" is  d%2F3  hours.


The time to go "back"  is  d%2F5  hours.


The total time is 1 hour, which gives you an equation


d%2F3 + d%2F5 = 1    hour.


To solve it, multiply both sides by 15. You will get


5d + 3d = 15,   or   8d = 15,   d = 15%2F8.


So, one way distance is  15%2F8   miles.


Hence, the total distance to "there" and "back"  is  twice 15%2F8 miles,  or  15%2F4 mile = 33%2F4 miles.    ANSWER

Solved.

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

As a comment to the @Alan3354's post, the Michelson-Morley experiment was performed for the first time in the year 1887 -
it is NOT the mid of the 17-th century; it is at the end of the 19-th century.

See this Wikipedia article
https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if a man walks a distance at 3 mph and jogs back the same route at 5 mph and the trip takes one hour how many miles did he travel
-------------
Avg speed for a round trip = 2*R1*R2/(R1 + R2) where R1 and R2 are the 2 speeds.
The distance is not relevant if they are equal.
----
Avg speed = 2*3*5/(3+5) = 30/8 = 3.75 mi/hr
--> 3.75 miles round trip
------
This is the basis of the famous Michelson-Morley experiment in the mid-17th century that disproved the existence of the "ether."
google it.
Learn something.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is yet another way to solve the problem.

As tutor @ikleyn states in her response, it is always worthwhile to know different ways to solve problems. In a particular problem, one method might be far easier to use than another.

The distances both ways are the same, and the ratio of the rates is 3:5. That means the ratio of the times is 5:3.

So the man spent 5/8 of the time at the lower rate and 3/8 of the time at the higher rate.

Since the total time was 1 hour, he spent 5/8 of an hour at 3mph, traveling (5/8)*3 = 15/8 miles; and he spent 3/8 of an hour at 5mph, traveling (3/8)*5) = 15/8 miles.

So the total distance he traveled is 15/8+15/8 = 15/4 miles.