## zello Group Title 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? one year ago one year ago

1. geoffb Group Title

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

2. geoffb Group Title

Remember the formula $$d = vt$$.

3. geoffb Group Title

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

4. zello Group Title

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

5. geoffb Group Title

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

6. geoffb Group Title

But that formula wouldn't apply for this question.

7. zello Group Title

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

8. zello Group Title

?

9. geoffb Group Title

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 Group Title

So V for both will be 12 ?

11. geoffb Group Title

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 Group Title

No, V cannot be 12 for both.

13. zello Group Title

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

14. geoffb Group Title

No.

15. geoffb Group Title

He doesn't bike at a velocity of 12.

16. zello Group Title

he rides 12 miles per hour faster than he jogs

17. geoffb Group Title

Yes! There you go.

18. zello Group Title

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

19. geoffb Group Title

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 Group Title

" rides 12 miles per hour FASTER THAN" he jogs

21. geoffb Group Title

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

22. zello Group Title

nope

23. geoffb Group Title

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

24. geoffb Group Title

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

25. Chlorophyll Group Title

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

26. geoffb Group Title

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

27. Bronco101 Group Title

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 Group Title

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

29. geoffb Group Title

Your times are right, but not your velocities.

30. geoffb Group Title

V-jog is wrong.

31. geoffb Group Title

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

32. zello Group Title

Okay

33. zello Group Title

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

34. geoffb Group Title

Yes! Good.

35. zello Group Title

now what ?

36. geoffb Group Title

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

37. geoffb Group Title

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

38. geoffb Group Title

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 Group Title

Ok

40. zello Group Title

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

41. geoffb Group Title

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

42. zello Group Title

I just solve V jog

43. Chlorophyll Group Title

@zello something isn't right with your calculation !

44. geoffb Group Title

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

45. geoffb Group Title

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

46. geoffb Group Title

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

47. zello Group Title

I'm a girl -_-

48. geoffb Group Title

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

49. geoffb Group Title

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

50. Chlorophyll Group Title

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

51. geoffb Group Title

@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 Group Title

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

53. geoffb Group Title

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 Group Title

how can i found the distance then

55. zello Group Title

find *

56. geoffb Group Title

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

57. zello Group Title

d= vt d jog= d bike

58. geoffb Group Title

Top one.

59. zello Group Title

vt jog = vt bike

60. geoffb Group Title

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

61. zello Group Title

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

62. geoffb Group Title

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 Group Title

Excellent job working through this.

64. Chlorophyll Group Title

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

65. zello Group Title

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

66. Hero Group Title

I got 2.8 exactly with my methods.

67. geoffb Group Title

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 Group Title

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

69. zello Group Title

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

70. Chlorophyll Group Title

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

71. zello Group Title

it's not exact in my calculator

72. Chlorophyll Group Title

So you're unable to calculate the fraction?

73. zello Group Title

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

74. Chlorophyll Group Title

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 Group Title

There's nothing to round off :)

76. zello Group Title

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

77. zello Group Title

However, thank you