anonymous
  • anonymous
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?
Mathematics
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SOLVED
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katieb
  • katieb
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lgbasallote
  • 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
  • lgbasallote
oops i did something wrong idk why
lgbasallote
  • 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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lgbasallote
  • lgbasallote
@ganeshie8 did i do it right? im smelling negative time -_-
anonymous
  • anonymous
hmmm im not getting you
anonymous
  • anonymous
@ganeshie8 do you understand this one? i need your help.
ganeshie8
  • ganeshie8
4t-9 = 3t solve for t
lgbasallote
  • lgbasallote
9?
ganeshie8
  • ganeshie8
wait.. checking im also haunted by -ves... lol
anonymous
  • anonymous
yes 9 there but then what? and to be honest i dont understand why you arranged that as you did...
lgbasallote
  • lgbasallote
lol =))) traumatized :))
anonymous
  • anonymous
haunted???traumatized??? what are yall talking about?
ganeshie8
  • ganeshie8
ok.. you unerstand straight lines in slope-intercept form ?
anonymous
  • anonymous
dont think so
anonymous
  • anonymous
you still working on it?
ganeshie8
  • 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
  • anonymous
yes
anonymous
  • anonymous
please continue
ganeshie8
  • 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
  • anonymous
yah
saranya
  • 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
  • vishweshshrimali5
I can surely help What we have to do is just to use the concept of relative velocity
vishweshshrimali5
  • vishweshshrimali5
FIrst of all, Find out what distance does first person travel in those 3 hours
vishweshshrimali5
  • 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
  • anonymous
hmm confusing
vishweshshrimali5
  • vishweshshrimali5
u start solving step by step . I am here to help u
anonymous
  • anonymous
ok well all i know is 3k per hour and 3 hours later equals a 9kmperhour advantage.
vishweshshrimali5
  • 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
  • vishweshshrimali5
Got this ?
anonymous
  • anonymous
yes he can over take him because he goes a bit faster got that
vishweshshrimali5
  • 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
  • anonymous
yes to eliminate that advantage
vishweshshrimali5
  • vishweshshrimali5
Now what distance B actually travelled during these 9 hours = 9 * 4 = 36 km
vishweshshrimali5
  • vishweshshrimali5
I hope I did that correctly ?
anonymous
  • anonymous
then the other guy went 9x3 = 27 + the 9 advantage =36 so they both tie at 36?
vishweshshrimali5
  • vishweshshrimali5
Of course
anonymous
  • anonymous
but a tie is not an overtake
vishweshshrimali5
  • 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
  • anonymous
wouldnt?
vishweshshrimali5
  • vishweshshrimali5
Yes ofcourse
anonymous
  • anonymous
hmm i think i lost you
vishweshshrimali5
  • vishweshshrimali5
What happened
anonymous
  • anonymous
i dont get the tie/overtake thing
vishweshshrimali5
  • 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
  • anonymous
hmm but to be technical the the answer would be a tiny bit over 36
vishweshshrimali5
  • vishweshshrimali5
Yes but that tiny but will be very very very close to 0
anonymous
  • anonymous
yes i see so 36 then
vishweshshrimali5
  • vishweshshrimali5
yes
vishweshshrimali5
  • vishweshshrimali5
did that help u ?
anonymous
  • anonymous
yes very much thank you i may message you one like this but a bit harder

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