Question

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?

Answer 1

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

Answer 2

oops i did something wrong idk why

Answer 3

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

Answer 4

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

Answer 5

hmmm im not getting you

Answer 6

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

Answer 7

4t-9 = 3t

solve for t

Answer 8

9?

Answer 9

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

Answer 10

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

Answer 11

lol =))) traumatized :))

Answer 12

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

Answer 13

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

Answer 14

dont think so

Answer 15

you still working on it?

Answer 16

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 ?

Answer 17

yes

Answer 18

please continue

Answer 19

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 ?

Answer 20

yah

Answer 21

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.

Answer 22

I can surely help

What we have to do is just to use the concept of relative velocity

Answer 23

FIrst of all,

Find out what distance does first person travel in those 3 hours

Answer 24

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

Answer 25

hmm confusing

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

Got this ?

Answer 30

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

Answer 31

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 ?

Answer 32

yes to eliminate that advantage

Answer 33

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

Answer 34

I hope I did that correctly ?

Answer 35

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

Answer 36

Of course

Answer 37

but a tie is not an overtake

Answer 38

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

Answer 39

wouldnt?

Answer 40

Yes ofcourse

Answer 41

hmm i think i lost you

Answer 42

What happened

Answer 43

i dont get the tie/overtake thing

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

yes i see so 36 then

Answer 48

yes

Answer 49

did that help u ?

Answer 50

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