Question 842428: A train travels at a rate of (2x+3) miles per hour. How many miles can it travel at that rate in (x-4) hours?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula is:
rate * time = distance.
since your rate is equal to (2x+3) and your time is equal to (x-4), then the distance traveled will be equal to (2x+3) * (x-4).
you will travel different distances depending on the value of x.
your equation is:
y = (2x+3) * (x-4).
since the rate can't be less than 0 and the time can't be less than 0, then x has to be greater than or equal to 4.
when x = 4, the number of hours you have traveled is 0 and you have traveled 0 miles.
when x = 5, the number of hours you have traveled is 1 and the rate you are traveling at is 5 miles per hour, so you have traveled 5 miles.
you can create a table to capture the different number of hours and the resulting miles per hour and the resulting distance.
the equation for the distance traveled would be:
y = (2x+3) * (x-4).
that graph is shown below:
you can see from the graph that x has to be greater then 4 in order for the distance traveled to be positive.
this graph shows you the number of hours traveled and the distance traveled.
it does not show you the rate of speed.
the number of hours traveled is equal to x-4.
you have to keep that in mind.
x is not the number of hours traveled.
x-4 is.
sometimes a graph is good to see what's happening.
sometimes a table is.
here, a table might be better.
the following table tracks the number of hours traveled and the rate of speed and the distance traveled.
time rate distance
x x-4 2x+3 (x-4)*(2x+3)
4 0 11 0
5 1 13 13
6 2 15 30
7 3 17 51
8 4 19 76
9 5 21 105
10 6 23 138
11 7 25 175
12 8 27 216
13 9 29 261
14 10 31 310
15 11 33 363
16 12 35 420
17 13 37 481
18 14 39 546
19 15 41 615
20 16 43 688
21 17 45 765
22 18 47 846
23 19 49 931
24 20 51 1020
25 21 53 1113
when x = 15, the table says the distance traveled is 363 miles and the number of hours traveled is 11 and the rate of speed is equal to 33 miles per hour.
the table shows all the figures used.
the graph just shows the value of x and the distance traveled.
you have to translate the value of x to the number of hours traveled by subtracting 4 from it.
in this case, the table is clearer because it gives you all the pertinent data in one shot.
a horizontal line at y = 363 was shown on the graph to highlight the fact that when x = 15, y = 363. this may or may not be easy for you to see. Just look at the intersection point of the horizontal line with the graph and then draw a vertical line down to the x-axis and you will see that the value of x is 15 at that point. It's not all that easy to see. The table is clearer.
The bottom line on your equation is that you don't have enough information to get one answer.
you will get many depending on the value of x.
you would need some other information, such as what is the rate of speed when the car has traveled for 10 hours.
In that case, you will be able to find the distance traveled and the rate of speed.
the answer to that question would be:
when the car travels for 10 hours, the rate of speed is equal to 31 miles per hour and the distance traveled is 310 miles.
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