Question

A goods train 158 metres long, leaves Delhi at 6 a.m and travels at an average speed of 32 km/hr. A mail train 130 metres long, leaves Delhi at 12 noon and follows the goods train travelling at an average speed of 80 km/hr. At what time and at what distance from Delhi will the mail train completely cross the goods train?

Answer 1

length1=158,speed 32km/hr.length2=130,time1=x,time2=x-6,speed2=80km/hr

Answer 2

32*x=80*(x-6)

Answer 3

x=10

Answer 4

@anteater

Answer 5

@anteater ,hahha

Answer 6

158 meters long :)

Answer 7

LOL ... I am thinking about it!

Answer 8

And the other guy is replying, so I will continue on paper and verify what he says. :)

Answer 9

Okay, so the first train is 158meter, 32 mph. LEAVES at 6:00 am
the second train is 130meter, 80mph. LEAVES at 12 noon (6 hours after the 1st train).

(All the above is referring to where the very back of each train is)
You know that the 1st train is 6 hours ahead, which is in distance `32 × 6` and equals 192 miles.

So the first train is 192 miles ahead.
So now they are traveling the same direction and when will the second train (the one that travels faster) be equal (equal with fronts, not equal with the backs of the trains)?

Let x be number of hours.
192 + 32x = 80x
192 =48x
x=4

So thus the trains' backs will be at the same distance (from Delhi) after 4 hours.
Keep in mind though, that the firs train is 158 meters long, and the second is 130 meters long.
All you have left is to calculate the short time during which the second train is getting from being even by the backs, to being even by the fronts.

Answer 10

Let me know if you need help calculating that.

Answer 11

Actually, since it says the second train has to clear the first train, I think they mean the back of the second train will have to be even with the front of the first train. Correct me if I am mistaken, please.

Answer 12

Well.... yeah, perhaps the backs have to be even. Then it is simpler :)

Answer 13

No, I didn't mean the backs have to be even. :) I meant that the back of the second train has to be even with the nose of the first train, since it wants to know at what distance it will "completely cross" the goods train.

Answer 14

srry,322 meters 192+130

Answer 15

So by "completely cross", do they mean it is even with the first train (nose and nose) or entirely ahead of the first train?

Answer 16

well.... sounds like the first train has to be completely behind the second one.
I can't say this for sure though.

Answer 17

I wonder if they give a diagram with this problem so we could know for sure what they meant. dg2, do they have a picture of the trains?

Answer 18

nope @anteater

Answer 19

By any chance do they give the answer so that you can verify the approach?

Answer 20

You could work it out both ways, I suppose, and tell your instructor that since the directions weren't clear you did it both ways. :)

Answer 21

k tell me

Answer 22

So you could figure it one way, where the fronts of the trains are even. And then, you could do it another way where the back of the second train is even with the front of the first train. Extra work, I know ... but maybe they would give you extra credit? Never hurts to ask! :D

Answer 23

Sorry ... had to step away for a moment. Please let me know what you got for the nose-to-nose trains and/or what you got for the scenario where the second train is ahead of the first. I can double check. :)

Answer 24

oh i dont know how yo do that @anteater

Answer 25

Just a moment, please :)

Answer 26

this sum is boring :-)

Answer 27

Sorry!

Answer 28

Working on a drawing

Answer 29

k

Answer 30

I think they want the back of the second train to be even with the front of the first train, really.

Answer 31

The more I think about it, the more I am sure that is what they want.

Answer 32

So ... just a moment, please.

Answer 33

we can close this problem .later we do.shall we move on to next prob

Answer 34

Sure - if you want, I can work on this one and email you later?

Answer 35

And we can compare

Answer 36

yea!3q frnd

Answer 37

then.......

Answer 38

shall we move to next

Answer 39

Sure :)

Answer 40

do u know simple interest

Answer 41

Yes P = rt

Answer 42

Oops

Answer 43

I = Prt ... don't know what I was thinking there!

Answer 44

Robin lends Rs.9 to Rahul on the condition that the loan is repayable in 10 months in 10 equal installments of Re.1 each. Find the rate of interest per annum.

Answer 45

1=9*10*r/100
r=100/90=10/9

Answer 46

simple interest=pricipal*rate *time/100

Answer 47

is it correct?

Answer 48

Yes, that should be correct.

Answer 49

but in options 22*1/3,25*2/3,26*2/3,28*1/3

Answer 50

Give me a moment to think on this one. They have thrown a twist in here by making the loan due in 10 months, rather than 1 year.

Answer 51

I think we could work backward on it by starting with the payment. They say that you pay back 1 Re. each in 10 installments in 10 months.

Answer 52

So, how much money do you pay altogether?

Answer 53

9*10*r/100*12

Answer 54

total rs10

Answer 55

Right. But the principal amount was Re.9, so how much total interest was paid?

Answer 56

1

Answer 57

So you paid 1/9 of what you borrowed in 10 months. I think we could set up a ratio to solve it.

Answer 58

1/9/ 10 = x/12

Answer 59

Nope! I am thinking wrong on this.

Answer 60

yes

Answer 61

we can ask help with @ganeshie8

Answer 62

I think that would be a very good idea! :D

Answer 63

are u guys working on this problem :

` Robin lends Rs.9 to Rahul on the condition that the loan is repayable in 10 months in 10 equal installments of Re.1 each. Find the rate of interest per annum.`

?

Answer 64

Yes

Answer 65

yes

Answer 66

p+p*r*t/100*12

Answer 67

annual instalment formula=100*p/100*n+n*(n-1)/2

Answer 68

Thank you!

Answer 69

but didnt get the answer

Answer 70

Hmm.

Answer 71

Found this: http://www.math.wsu.edu/students/aredford/documents/Notes_Installments.pdf

Answer 72

im getting interest rate as 23.5%
http://www.wolframalpha.com/input/?i=solve+1+%3D+%289*r%2F12%281%2Br%2F12%29%5E%2810%29%29%2F%28%281%2Br%2F12%29%5E%2810%29-1%29+in+reals

Answer 73

used this formula
http://phfcl.org.in/files/resized/227871/294;114;119ac1faced6dbe224029d9fe737c2128c9fc6eb.jpg

Answer 74

I have a question, though ... would that be annually compounded interest or simple interest for that formula?

Answer 75

compounded every month on the balance amount

Answer 76

at the end of first month, balance = 9 + (23.5% of 9)
Robin pays 1 rupee, so balance reduces to : 8 + (23.5% of 9)

Answer 77

this cycle repeats every month

Answer 78

That makes sense.