## A community for students. Sign up today

Here's the question you clicked on:

## countonme123 3 years ago 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?

• This Question is Closed
1. 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

2. lgbasallote

oops i did something wrong idk why

3. 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

4. lgbasallote

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

5. countonme123

hmmm im not getting you

6. countonme123

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

7. ganeshie8

4t-9 = 3t solve for t

8. lgbasallote

9?

9. ganeshie8

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

10. countonme123

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

11. lgbasallote

lol =))) traumatized :))

12. countonme123

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

13. ganeshie8

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

14. countonme123

dont think so

15. countonme123

you still working on it?

16. 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 ?

17. countonme123

yes

18. countonme123

please continue

19. 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 ?

20. countonme123

yah

21. 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.

22. vishweshshrimali5

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

23. vishweshshrimali5

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

24. 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

25. countonme123

hmm confusing

26. vishweshshrimali5

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

27. countonme123

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

28. 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

29. vishweshshrimali5

Got this ?

30. countonme123

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

31. 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 ?

32. countonme123

yes to eliminate that advantage

33. vishweshshrimali5

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

34. vishweshshrimali5

I hope I did that correctly ?

35. countonme123

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

36. vishweshshrimali5

Of course

37. countonme123

but a tie is not an overtake

38. 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

39. countonme123

wouldnt?

40. vishweshshrimali5

Yes ofcourse

41. countonme123

hmm i think i lost you

42. vishweshshrimali5

What happened

43. countonme123

i dont get the tie/overtake thing

44. 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

45. countonme123

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

46. vishweshshrimali5

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

47. countonme123

yes i see so 36 then

48. vishweshshrimali5

yes

49. vishweshshrimali5

did that help u ?

50. countonme123

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

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy