Question

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?

Answer 1

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

Answer 2

Remember the formula \(d = vt\).

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

But that formula wouldn't apply for this question.

Answer 7

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

Answer 8

?

Answer 9

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:

\[\begin{align*}
v_{jog} &=
\\ v_{bike} &=
\\t_{jog} &=
\\t_{bike} &=
\end{align*}\]

Answer 10

So V for both will be 12 ?

Answer 11

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.

Answer 12

No, V cannot be 12 for both.

Answer 13

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

Answer 14

No.

Answer 15

He doesn't bike at a velocity of 12.

Answer 16

he rides 12 miles per hour faster than he jogs

Answer 17

Yes! There you go.

Answer 18

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

Answer 19

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.

Answer 20

" rides 12 miles per hour FASTER THAN" he jogs

Answer 21

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

Answer 22

nope

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

Your times are right, but not your velocities.

Answer 30

V-jog is wrong.

Answer 31

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

Answer 32

Okay

Answer 33

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

Answer 34

Yes! Good.

Answer 35

now what ?

Answer 36

Now solve for \(v_{jog}.\)

Answer 37

And remember—the v on the right side is also \(v_{jog}\).

Answer 38

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.

Answer 39

Ok

Answer 40

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

Answer 41

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

Answer 42

I just solve V jog

Answer 43

@zello something isn't right with your calculation !

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

I'm a girl -_-

Answer 48

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

Answer 49

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

Answer 50

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

Answer 51

@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.

Answer 52

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

Answer 53

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.

Answer 54

how can i found the distance then

Answer 55

find *

Answer 56

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

Answer 57

d= vt
d jog= d bike

Answer 58

Top one.

Answer 59

vt jog = vt bike

Answer 60

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

Answer 61

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

Answer 62

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.

Answer 63

Excellent job working through this.

Answer 64

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

Answer 65

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

Answer 66

I got 2.8 exactly with my methods.

Answer 67

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

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

it's not exact in my calculator

Answer 72

So you're unable to calculate the fraction?

Answer 73

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

Answer 74

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

Answer 75

There's nothing to round off :)

Answer 76

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

Answer 77

However, thank you