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

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)   (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

If you need additional help, please follow us on Instagram or message us via social media! We also help with SAT Math Questions!

***Instagram (@mathsolver.plus): https://www.instagram.com/mathsolver.plus/
Twitter (@MathSolverPlus): https://twitter.com/MathSolverPlus
Snapchat (@mathsolverplus)
Email: mathsolverplus@gmail.com
Answer by ikleyn(52803)   (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 hours. The time to go "back" is hours. The total time is 1 hour, which gives you an equation + = 1 hour. To solve it, multiply both sides by 15. You will get 5d + 3d = 15, or 8d = 15, d = . So, one way distance is miles. Hence, the total distance to "there" and "back" is twice miles, or mile = 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)   (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)   (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.
RELATED QUESTIONS
A person jogs a certain distance at a rate of five mph and gets a ride back over the same (answered by Boreal)
Anabelle runs the same route every day. She runs part of the way and jogs part of the... (answered by mananth)
If David walks at the rate of 5 mph and jogs at the rate of 9 mph and it takes 2 hours to (answered by oscargut)
if a man travels at 3 mph from point A to point B and then travels back from point B to... (answered by richwmiller)
Maria jogs to the country at a rate of 10mph . She returns along the same route at 6... (answered by checkley79)
A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and... (answered by stanbon)
2 LINEAR EQUATIONS IN 2 UNKNOWNS or SIMULTANEOUS LINEAR EQUATIONS IN 2 UKNOWNS A... (answered by josgarithmetic)
If David walks at the rate of 5 mph and jogs at the rate of 9 mph and it takes 3 hours to (answered by richwmiller)
A fisherman takes his boat out to sea and then back to the harbor. The entire trip lasts (answered by pushpaharan)