Question

I need help with this question:

A car completes a journey at an average speed of 40 km/h. At what speed must it travel on the return journey if the avg. speed for the complete journey (out and back) is 60 km/h?

(I'm confused with the question, so explain it step by step please)

Answer 1

Here is what it is saying:
\[\text{A car travels from point A to B, and back to B}\]\[\text{The speed he drives at from Point A to B is 40km/h}\]\[\text{The average speed he drives from Point A to B, and back to A is 60km/h}\]
Do you understand that, @zGrimReaper123 ?

Answer 2

\[\text{They want you to find the speed from Point B to Point A}\]

Answer 3

Do you, @zGrimReaper123?

Answer 4

Yeah

Answer 5

But can you explain it bit by bit? I'm not really great at maths

Answer 6

Its fine. I just want to know if you understand the above completely?

Answer 7

If you don't understand ANYTHING, just say so.

Answer 8

I don't understand anything

Answer 9

Ok, Imagine there is a car. He is going from one place to another.
He is going at a speed of 40km/h

Answer 10

Lets say the first place is Point A, the second place is Point B

Answer 11

I get that part

Answer 12

I'm just unsure of how I'm supposed to calculate the whole thing

Answer 13

Ok. Have you heard of this equation:
\[Average=\frac{Total 1 + Total 2 + Total 2+ Total 4...}{\text{Number of Totals}}\]

Answer 14

Yup

Answer 15

Does it mean average speed is equal to total distance divided by total time?

Answer 16

Yes, The issue there is that we are not given the time OR distance :(

Answer 17

So we must try another way

Answer 18

Right

Answer 19

Good. Now you know these informatin:
\[\text{The First Total(Speed)}\]\[\text{How many totals there are (2)}\]
Now, we don't know the speed of the car that is travelling back, so let that be \(x\)

Answer 20

Ok...

Answer 21

Why are you confused?

Answer 22

I'm not, I'm just agreeing

Answer 23

To your point

Answer 24

Oh, phew ;)

Answer 25

Yeah hehe

Answer 26

Average Equation:\[Average=\frac{Total1+Total2+Total2+Total4...}{Number of Totals}\]
Sub in the Average Speed, The First Speed, The Second Speed, and the number of totals:
\[60km/h=\frac{40km/h+x}{2}\]
Remove the the \(km/h\)
\[60=\frac{40+x}{2}\]

Answer 27

Do you understand that?

Answer 28

What does sub stand for?

Answer 29

Substitue in. Pretty much, put information inside.

Answer 30

Right

Answer 31

I mean, I already know the answer is 120, I just want to know the method, and so far you're really helpful

Answer 32

Now, lets find what \(x\) is, which we said was the speed of the return trip
\[60km=\frac{40km+x}{2}\]
Now to remove the 2 on the right hand side, we need to do the opposite of what the 2 is doing, In this equation, it is dividing. Therefore, we need to multiply both sides by 2.
\[60*2=\frac{40+x}{2}*2\]
\[120=40+x\]
Now, move the 40 to the left hand side. Since in this example it is adding 40, we need to take away 40 on both sides.
\[120-40=40+x-40\]
\[80=x\]\[x=80\]
Therefore, the speed when he came back was \(80km/h\)

Answer 33

Does that make sense, @zGrimReaper123?

Answer 34

Yes, but are you sure the answer is 80 km/h?

Answer 35

According to my calculations yeah, why?

Answer 36

@hartnn, if you can clarify on the question please?

Answer 37

The question I'm talking about was taken from a book I'm using, and the answer for it is written at the back, which is 120km/h, not 80km/h

Answer 38

Finally my pc decided to send it, it was hanging

Answer 39

Hmm. From my calculations, it cannot be. However, I might be missing something...

Answer 40

Yeah, probably

Answer 41

It can't be though. Since the 60 is the average speed, and the equation:
\[Average=\frac{Total1+Total2...}{\text{Number of Totals}}\]
If we were to sub in the values 40, 2 and 120(Your answer)
\[60=\frac{40+120}{2}\]
\[60=\frac{160}{2}\]
\[60=80\]
Thats impossible. Either I missed some crucial information, or the book is wrong.

Answer 42

40+80=120/2 wud give u an avg speed of 60
but 40+120=160/2 wud give u and avg speed of 80
so i guess@Ahsome is right the ans is 80 and not 120

Answer 43

average speed = total distance / total time

Answer 44

We don't know distance OR time. So what we do?

Answer 45

assume some variables

Answer 46

@Ahsome Perhaps you're right. I wrote down the entire question, so probably your calculations are correct after all

Answer 47

Or maybe not

Answer 48

Thanks @zGrimReaper123. If I figure out the difference, I will tell you. I am guessing they forgot to take away 40, which gave 120 as an answer.

Answer 49

I guess so

Answer 50

A -> B

Speed = 40km/hr
Distance = D

time = D/40 hrs.

A->B->A

Speed = 60 km/hr
Distance = 2D
time = 2D/60 hrs

Answer 51

B->A
Speed = x
Distance = D
time = D/x

find x

Answer 52

60 = 2D/ (D/40 + D/x)

Answer 53

60 = 2/ (1/40+1/x)

find x

Answer 54

Is this it?
\[60=\frac{2}{\frac{1}{40}+\frac{1}{x}}\]

Answer 55

you will indeed get x=120
which is correct

Answer 56

the catch here was to apply the formula
avg. speed = total distance / total time

total distance = D+D
total time

= time from A->B + time from B->A
= D/40 +D/x

Answer 57

Cross Multiply?
\[60*(\frac{1}{40}+\frac{1}{x})=2*1\]

Answer 58

yep

Answer 59

\[\frac{60}{240}+\frac{60}{60x}=2\]

Answer 60

simpler way to do it will be

1/x = 1/30 -1/40

Answer 61

Get everything to have the same base
\[\frac{60}{240}*\frac{x}{x}+\frac{60}{60x}*\frac{4}{4}=\frac{2}{1}*\frac{240}{240}\]

Answer 62

\[\frac{60x}{240x}+\frac{240}{240x}=\frac{420}{240x}\]
Cut the \(240x\)

Answer 63

\(60x+240=480\)
\(60x=240\)
\(x=4\)

Answer 64

Now what?

Answer 65

wot ? O.o

what have you done ?

Answer 66

I must have made some HUGE mistake. Anyway ;)

Answer 67

I see where I made a mistake, I also times the denominator ;)

Answer 68

60 (1/40 +1/x) = 2

1/40 +1/x = 2/60 = 1/30

1/x = 1/30 - 1/40 = (40-30)/1200 = 10/1200 = 1/120

x=120

Answer 69

hopefully @zGrimReaper123 understood all this ;)

Answer 70

important thing is to get this equation

avg speed = total distance / total time
60 = 2D/ (D/40 + D/x)

then its pretty algebraic.

Answer 71

Yes, @hartnn, yes it is ;)

Answer 72

Do you need us to reexplain that, @zGrimReaper123?

Answer 73

@Ahsome Maybe, just let me read the explanation again. I was away while you guys were at it

Answer 74

@Ahsome @hartnn I really appreciate your help :D

Answer 75

No problem. Thank @hartnn, I went on some tangent ;)

Answer 76

no i have an easy way to solve this

Answer 77

:D

Answer 78

u are so good ahsome

Answer 79

how are u

Answer 80

@TheGreatStupidPerson Please tell me the easier way

Answer 81

you can ask your father if he is good at studies

Answer 82

ahsome is your grandmother alive

Answer 83

@TheGreatStupidPerson Are you fluttering serious?

Answer 84

what saying me not understandings

Answer 85

no teej me ok

Answer 86

i will complaint your teacher if u teej me

Answer 87

now leave your studies and let have a break

Answer 88

@TheGreatStupidPerson Can you piss off somewhere else?

Answer 89

for enjoyment i will tell u a story of a princess ok

Answer 90

@Ahsome

Answer 91

@Ahsome Are we able to chat privately?

Answer 92

you can ask your teacher if she knows the correct answer

Answer 93

@zGrimReaper123 why is your name say that u are a raper and u rape women