SOLUTION: B travels from home to school at 6km/h and returns same route at 8km/h in 70 minutes for entire joruney. What is the distance of school A man travels certain distance at 30km/h

Question 1038787: B travels from home to school at 6km/h and returns same route at 8km/h in 70 minutes for entire joruney. What is the distance of school
A man travels certain distance at 30km/h and returns same route at 50kmh\.h and takes 5 hours for entire journey what is the total distance
Found 5 solutions by josgarithmetic, josmiceli, MathTherapy, Alan3354, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
These are two examples of the same problem.

Traveler goes to destination at g rate and returns on same route at r rate, and the entire journey is t hours. Find the distance in either direction.

A table of data is very helpful to make.

SPEED TIME DISTANCE GO g d/g d BACK r d/r d Total t

Your first example uses , and you can compute d, once you solve for it in symbols.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = distance from home to school
Let = time in hrs B takes at 6 km/hr
-------------------------------------
(a)
(1)
(2)
--------------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)
and
(1)
(1)
(1)
The distance from home to school is 4 km
---------------------------------------
(b)
(1)
(2)
---------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)
and
(1)
(1)
(1)
(1)

the total distance is 187.5 km
---------------------------
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
(2)
OK
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

B travels from home to school at 6km/h and returns same route at 8km/h in 70 minutes for entire joruney. What is the distance of school
A man travels certain distance at 30km/h and returns same route at 50kmh\.h and takes 5 hours for entire journey what is the total distance

Let distance be D
Then time taken to travel from home to school = , and time taken on return trip =
We then get the following TIME equation: ________
4D + 3D = 28 ------- Multiplying by LCD, 24
7D = 28
D, or distance = , or
One (1) question per post. Hint: 2nd is done the same way as the 1st. Good practice for you, I'm sure.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
B travels from home to school at 6km/h and returns same route at 8km/h in 70 minutes for entire joruney. What is the distance of school
----------
Avg speed of a round trip is similar to parallel flow and parallel resistors.
-----
Avg = 2*r1*r2/(r1+r2)
= 2*6*8/14 = 96/14 km/hr
----
70 mins = 7/6 hours
RT distance = (48/7)*(7/6) = 8 km
4 km one way.
------------------
I don't try to remember all the formulas there are, but this one is easy, only a factor of 2 difference from flow, work or resistance in parallel.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
See the lesson Calculating an average speed: a train going from A to B and back in this site.

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