Question

I JUST CAN'T get the hang of these. In tears!

Two cyclists leave towns 76 mi apart at the same time and travel toward each other. One cyclist travels 6 mph faster than the other. If they meet in 2 hours, what is the rate of each cyclist?

Answer 1

what is rate of speed of cyclist 1?

Answer 2

umm... I need to figure the rate of both bikes

Answer 3

well the answer is i do not know

so we would let that be x
cyclist 2 would x+6
you know the time 2 and the distance 76
2x+2(X+6) = 76 solve this for x

Answer 4

You could also think about it like this:

since there are 2 cyclists and 1 is traveling FASTER than the other, then let:

cyclist 1 = x (the one that's moving slower)

cyclist 2 = x+6 (this guy is travelling 6 miles FASTER than the first guy)

Answer 5

2x + 2(x+6) = 76
2x + 12 = 76

Answer 6

2x + 2(x+6) = 76
2x +2x+ 12 = 76

Answer 7

2x + 2(x+6) = 76
2x + 12 = 76
12/76 = 6.333

Answer 8

As d = rt (distance = rate TIMES time) , and we know the rate of cyclist 1 and 2, then :

d\(_1\) = 70 mi = 2x

d\(_2\) = 2(x+6)

Answer 9

Combining these two, since they are both travelling the same distance, we get \[70 = 2x +2(x+6)\]

Answer 10

2x + 2(x+6) = 76
4x + 24 = 76

Answer 11

First of all, is what me and @zpupster making sense?

Answer 12

4x + 12 = 76

Answer 13

It's easy to plug and chug, but are you understanding the concept?

Answer 14

I think it is a rate x distance = time?

Answer 15

No.

distance = rate x time

Answer 16

That is why you are multiplying `2` to both rates,

Answer 17

2(x) and 2(x+6)

Answer 18

6 x 2 = Distance

Answer 19

Does 6 \(\times\) 2 = 70?

Answer 20

No 12

Answer 21

this was right just solve for x
4x + 12 = 76

Answer 22

x = 76 - 12

Answer 23

No.

Answer 24

4x = 76 - 12*

Answer 25

4x = 76 - 12

Answer 26

x = 76 + 12
x = 88

Answer 27

4/88=11

Answer 28

That is wrogn.

Answer 29

x = 11
11+ 6 = 17 faster

Answer 30

You don't really seem like you know what you are doing.

Answer 31

I have been trying for a week. My teacher is ignoring me

Answer 32

First of all, where did your 4 disappear to?

4x = 76 - 12 suddenly became x = 76 - 12

Answer 33

slow down faine
take a breath then let start with

4x = 76 - 12

Answer 34

That is why I am crying. I have been sitting here all day doing one after another and all were wrong

Answer 35

I divided my 4 into the 88 to get 11

Answer 36

I think what you are confused with starting from the top is understanding what the RATE of each cyclist is, and why one is labeled as x and the other is labeled as x+6.

Answer 37

x = 64
@zpupster

Answer 38

Once you understand that, you can associate that with the distance formula, d = rt, where the time for BOTH is 2 hours.

Answer 39

4x=64

Answer 40

yes

Answer 41

4/64 = 16

Answer 42

That's correct.

Answer 43

divide both sides by 4

Answer 44

Now you've got the rate of the slower cyclist.

Answer 45

16 + 6 = 22

Answer 46

All you need to do is figure out how much faster the other one is moving, which you just got as well.

Answer 47

good job!!!

Answer 48

Now retry this problem without looking.

Answer 49

Answer me this, what if the problem said `one cyclist is moving SLOWER than the other`?

Answer 50

w would you write the rate of cyclist #2?

Answer 51

How do I medal all of you? I can not believe my stupidity is this obvious and I am feeling dumb. I'm in friggin college for sanity sake! How did I get this far. THANK YOU ALL!!!!!!!

Answer 52

16 - 6 = 10 If it were 6 mph slower?

Answer 53

Awesome.

Answer 54

I hope these stay in my abccount so I can look back on what we did and try a few alone

Answer 55

And if the problem said they were moving against eachother, then you would subtract the rates.