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

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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) About Me  (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


d%2Fg%2Bd%2Fr=t

d%281%2Fg%2B1%2Fr%29=t

d%28r%2Bg%29%2F%28gr%29=t

highlight%28d=tgr%2F%28r%2Bg%29%29

Your first example uses system%28g=6%2Cr=8%2Ct=1%261%2F6%29, and you can compute d, once you solve for it in symbols.

Answer by josmiceli(19441) About Me  (Show Source):
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Let +d+ = distance from home to school
Let +t+ = time in hrs B takes at 6 km/hr
-------------------------------------
(a)
(1) +d+=+6t+
(2) +d+=+8%2A%28+70%2F60+-+t+%29+
--------------------------
(2) +d+=+560%2F60+-+8t+
Substitute (1) into (2)
(2) +6t+=+56%2F6+-+8t+
(2) +14t+=+28%2F3+
(2) +t+=+2%2F3+
and
(1) +d+=+6t+
(1) +d+=+6%2A%282%2F3%29+
(1) +d+=+4+
The distance from home to school is 4 km
---------------------------------------
(b)
(1) +d+=+30t+
(2) +d+=+50%2A%28+5+-+t+%29+
---------------------
(2) +d+=+250+-+50t+
Substitute (1) into (2)
(2) +30t+=+250+-+50t+
(2) +80t+=+250+
(2) +t+=+25%2F8+
and
(1) +d+=+30t+
(1) +d+=+30%2A%2825%2F8%29+
(1) +d+=+15%2A%28+25%2F4+%29+
(1) +d+=+93.75+
+2d+=+187.5+
the total distance is 187.5 km
---------------------------
check:
(1) +d+=+30t+
(1) +93.75+=+30%2A%2825%2F8%29+
(1) +750+=+30%2A25+
(1) +750+=+750+
and
(2) +d+=+50%2A%28+5+-+t+%29+
(2) +93.75+=+50%2A%28+5+-+25%2F8+%29+
(2) +93.75+=+250+-+50%2A%28+25%2F8+%29+
(2) +750+=+8%2A250+-+25%2A50+
(2) +750+=+2000+-+1250+
(2) +750+=+750+
OK

Answer by MathTherapy(10552) About Me  (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 = D%2F6, and time taken on return trip = D%2F8

We then get the following TIME equation: D%2F6+%2B+D%2F8+=+70%2F60________D%2F6+%2B+D%2F8+=+7%2F6

4D + 3D = 28 ------- Multiplying by LCD, 24

7D = 28

D, or distance = 28%2F7, or highlight_green%28matrix%281%2C2%2C+4%2C+km%29%29



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) About Me  (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) About Me  (Show Source):