## zello 2 years ago Kevin can jog to work in 7/12 of an hour. When he rides his bike, it takes him 1/6 of an hour. If he rides 12 miles per hour faster than he jogs, how far away is his work?

1. geoffb

It's the same idea as before. The distance to work doesn't change.

2. geoffb

Remember the formula $$d = vt$$.

3. geoffb

Since $$d$$ is the same no matter how he gets there, $$(vt)_{jog} = (vt)_{bike}$$.

4. zello

but I don't know why in sometimes it becomes d1+d2

5. geoffb

All I can think for that would be $$d_{1} + d_{2} = d_{total}$$

6. geoffb

But that formula wouldn't apply for this question.

7. zello

$vt 1=vt2$ $\frac{ 1 }{ 7 }t=\frac{ 1 }{ 6 } (12-t)$

8. zello

?

9. geoffb

Once you've determined what to equate (in this case, $$d$$), it's best to write out everything you need and see what you already know. That way, you know what to solve for. You're looking for $$(vt)_{jog} = (vt)_{bike}$$. There are 4 variables there: \begin{align*} v_{jog} &= \\ v_{bike} &= \\t_{jog} &= \\t_{bike} &= \end{align*}

10. zello

So V for both will be 12 ?

11. geoffb

You've used $$12 - t$$, which is not correct because the 12 relates to his velocity, not time. Go back to your question and see what you can plug in. You should end up with three answers (one will be relative), leaving one variable to solve for.

12. geoffb

No, V cannot be 12 for both.

13. zello

Okay so v bike = 12 and v jop= 12-t

14. geoffb

No.

15. geoffb

He doesn't bike at a velocity of 12.

16. zello

he rides 12 miles per hour faster than he jogs

17. geoffb

Yes! There you go.

18. zello

He will ride a bike 12 miles per hour and he will jog 12-t

19. geoffb

Nope. That's the same thing you said before. he does not bike at a speed of 12 mph. He bikes 12 mph *faster* than he jogs. You need to know how fast he jogs to know how fast he bikes.

20. Chlorophyll

" rides 12 miles per hour FASTER THAN" he jogs

21. geoffb

Have you plugged in your values for these? \begin{align*} v_{jog} &= \\ v_{bike} &= \\t_{jog} &= \\t_{bike} &= \end{align*}

22. zello

nope

23. geoffb

If he bikes 12 mph faster than he jogs, $$v_{bike} = v_{jog} + 12$$, right?

24. geoffb

That should get you started. There are two more values you can plug in.

25. Chlorophyll

@zello then you'd better fill it in, keep in mind the unit match with variable !

26. geoffb

Yes! Keeping track of units is crucial, as is remembering what your variable means when you're done.

27. Bronco101

all i can get is he jogs for 35 minutes, and rides for 10 minutes. He rides 2 miles faster per 10 minutes than he jogs O.O

28. zello

V bike= V jog+12 V jog = V bike-12 T jog =7/12 T bike = 1/6

29. geoffb

Your times are right, but not your velocities.

30. geoffb

V-jog is wrong.

31. geoffb

It's just V-jog. Don't equate it to anything. It will be the variable you solve for.

32. zello

Okay

33. zello

$vt Bike = vt Jog$ $\frac{ 1 }{ 6 }(vJog+12) =\frac{ 7 }{ 12 } v$

34. geoffb

Yes! Good.

35. zello

now what ?

36. geoffb

Now solve for $$v_{jog}.$$

37. geoffb

And remember—the v on the right side is also $$v_{jog}$$.

38. geoffb

Call it $$v$$, or $$x$$, or whatever you want. It's the same no matter how you approach it. If the subscript "jog" confuses you, omit it, but remember what $$v$$ represents.

39. zello

Ok

40. zello

$\frac{ 1 }{ 6 }(v+12)=\frac{ 7 }{ 12 }v$ $\frac{ 1 }{ 6 }v+2=\frac{ 7 }{ 12 }$ $\frac{ 1 }{ 6}v-\frac{ 7 }{ 12 }v=-2$ $0.16v-0.58=-2$ $-0.42 v=-2$ $v=4.76$

41. geoffb

I left my answers in fractions, so I'm not sure. What do you get for your final answer?

42. zello

I just solve V jog

43. Chlorophyll

@zello something isn't right with your calculation !

44. geoffb

No, that's not what the question wants. Go back and read the last sentence.

45. geoffb

@Chlorophyll It's just rounding error. I got $$v_{jog} = \frac{24}{5}$$, so I think he's okay.

46. geoffb

Although I only looked at his answer, not his work.

47. zello

I'm a girl -_-

48. geoffb

Oh, I'm sorry. I judge too quickly by avatars.

49. geoffb

Although that's obviously not you... :S

50. Chlorophyll

Yes, it's very neat V = 24/5 ( 4.8 mi/hr) @zello Better keep it in fraction form!

51. geoffb

@zello When you get to this stage: $\frac{ 1 }{ 6}v-\frac{ 7 }{ 12 }v=-2$ Multiply everything by 12 and simplify to get rid of the fractions.

52. zello

I have a headache because from 9 A.M until now, I still working on my math >.<

53. geoffb

Well, you've been working hard, and definitely showing growth. You're welcome to take a break, but you're almost done this question. Remember, we needed to find $$v_{jog}$$ to solve the equation, but $$v_{jog}$$ is not what the question asks for. It asks how far away his work is.

54. zello

how can i found the distance then

55. zello

find *

56. geoffb

You know your distance formula. We've used it a lot.

57. zello

d= vt d jog= d bike

58. geoffb

Top one.

59. zello

vt jog = vt bike

60. geoffb

No, just $$d = vt$$. You know $$v$$ now, and you already knew $$t$$, so solve for $$d$$.

61. zello

d bike = v bike * t bike d= 4.76 * 0.58 d= 2.7608

62. geoffb

Good. Don't forget your units. It's technically 2.8, so you're a bit off due to rounding errors, but that's right.

63. geoffb

Excellent job working through this.

64. Chlorophyll

@zello I wonder if you know how to say thanks by distributing the medal (?)

65. zello

Thank you so much and I'm sorry that I took a lot of your time. I really appreciate that

66. Hero

I got 2.8 exactly with my methods.

67. geoffb

Not a problem at all. Glad I could help. Thank you for making the effort to solve it on your own and learn.

68. Chlorophyll

Yup, that's why I say zello's calculation is incorrect!

69. zello

It' not incorrect, it's just because I didn't round my answer

70. Chlorophyll

It's exact, so there's no need to round!

71. zello

it's not exact in my calculator

72. Chlorophyll

So you're unable to calculate the fraction?

73. zello

I know how to calculate the fraction but the question says that they want the answer rounded to the nearest tenth

74. Chlorophyll

First, you should keep the number in fraction if it isn't exact result Second, in this case it's exact! 7v / 12 = ( v + 12 ) /6 (7/ 12 - 1/6)v = 2 -> v = 2 * 12/5 = 24/5 = 2.8 mi/ hr

75. Chlorophyll

There's nothing to round off :)

76. zello

when I calculate it, I didn't use the fraction

77. zello

However, thank you