One man starts out from a city and walks north at the rate of 3 kilometers per hour. Three hours later, a second man starts from the same place and walks the same route at 4 kilometers per hour. How far will he have to go before he overtakes the first man?

- anonymous

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- lgbasallote

let t = man A's time
t + 3 = man B's time
when he overtakes the guy they would be at the same distance from the starting point
d = speed x time
d of man A = 3t
d of man B = 4(t-1)
like i said if they overtake then distances are the same
3t = 4(t-1)
solve for t

- lgbasallote

oops i did something wrong idk why

- lgbasallote

d of man B = 4(t+3)
like i said if they overtake then distances are the same
3t = 4(t+3)
solve for t

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## More answers

- lgbasallote

@ganeshie8 did i do it right? im smelling negative time -_-

- anonymous

hmmm im not getting you

- anonymous

@ganeshie8 do you understand this one? i need your help.

- ganeshie8

4t-9 = 3t
solve for t

- lgbasallote

9?

- ganeshie8

wait.. checking im also haunted by -ves... lol

- anonymous

yes 9 there but then what? and to be honest i dont understand why you arranged that as you did...

- lgbasallote

lol =))) traumatized :))

- anonymous

haunted???traumatized??? what are yall talking about?

- ganeshie8

ok.. you unerstand straight lines in slope-intercept form ?

- anonymous

dont think so

- anonymous

you still working on it?

- ganeshie8

ok..
as @lgbasallote said, distance is same here right.
distance travelled by First man in time t = 3t
in 3 hours he would have travelled 9 km
so 9km is the distance second man lags when he starts his run.
he is running at 4t speed. so at any point he will be covering (4t-9km) distance
so far does it make sense ?

- anonymous

yes

- anonymous

please continue

- ganeshie8

so, now we can equate the distance and get the value of t.
distance travelled by first man : 3t
distance travelled by second man : 4t-9
4t-9 = 3t
=> t = 9 hours
so, after 9 hours, both guys would have travelled the same distance.
but question is asking about the distance second man has to travel before he overtakes first man, right ?

- anonymous

yah

- saranya

You can do this in two ways, do it in one way and check it using the second way.
The first is to use the speed/distance/time formula and the second is to use a velocity-time graph and use the areas.

- vishweshshrimali5

I can surely help
What we have to do is just to use the concept of relative velocity

- vishweshshrimali5

FIrst of all,
Find out what distance does first person travel in those 3 hours

- vishweshshrimali5

Now second person has to travel this distance + some more distance.
Now relative velocity of second person wrt first person = 4-3 km/h = 1 km/h
Now he has to travel a distance equal to distance travelled by first person in 3 h and that also with a relative speed of 1 km/h. From here find out the time

- anonymous

hmm confusing

- vishweshshrimali5

u start solving step by step .
I am here to help u

- anonymous

ok well all i know is 3k per hour and 3 hours later equals a 9kmperhour advantage.

- vishweshshrimali5

Only 9 km advantage in this 3 hour interval.
Now use the concept of relative velocity
First person let A is moving with 3 km/h
Second person say B is moving with 4 km/h
So B has an advantage of 1 km/h
Right ?
This is the relative velocity of B w.r.t A

- vishweshshrimali5

Got this ?

- anonymous

yes he can over take him because he goes a bit faster got that

- vishweshshrimali5

Yes gud
Now overall B has to travel 9 km at a speed of 1 km/h
Right, I am taking relative speed here as that will help me in assuming that A is at rest.
Now,
time taken by B to travel these 9 km = 9 h
Got this ?

- anonymous

yes to eliminate that advantage

- vishweshshrimali5

Now what distance B actually travelled during these 9 hours = 9 * 4 = 36 km

- vishweshshrimali5

I hope I did that correctly ?

- anonymous

then the other guy went 9x3 = 27 + the 9 advantage =36
so they both tie at 36?

- vishweshshrimali5

Of course

- anonymous

but a tie is not an overtake

- vishweshshrimali5

It is not that dear,
If you have tied it than it will not even take a second for B to overtake A as he has an advantage of 1 km/h speed so that wouldn't be right to tell when B will overtake

- anonymous

wouldnt?

- vishweshshrimali5

Yes ofcourse

- anonymous

hmm i think i lost you

- vishweshshrimali5

What happened

- anonymous

i dont get the tie/overtake thing

- vishweshshrimali5

See If I say u that me and u r having a race
I was ahead of u when u started but u started with a higher speed
A time came when I and U were at same point but as you are having more speed than me
U will easily overtake me even without taking a second after the tie point
Got this ?
So, that's why in such case we calculate the tie point as obviouslly after a very small time u will be ahead of me

- anonymous

hmm but to be technical the the answer would be a tiny bit over 36

- vishweshshrimali5

Yes but that tiny but will be very very very close to 0

- anonymous

yes i see so 36 then

- vishweshshrimali5

yes

- vishweshshrimali5

did that help u ?

- anonymous

yes very much thank you
i may message you one like this but a bit harder

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