Question

Two freight trains are delivering cargo. One freight train is delivering coal, and the other freight train is delivering grain. Their
respective distances traveled after x hours is represented in the table and graph below.
y
Grain Freight Train
405
360
315
Σ 270
Coal Freight Train
Time Distance Traveled
(Hours) (Miles)
1
48
2
96
3
144
4
192
225
180
135
8 90
45
0 1 2 3 4 5 6 7 8 9 ►
Time (Hours)
Which freight train is traveling at a faster speed?
OA. Both freight trains are traveling at the same speed.
ОВ.
The coal freight train is traveling at a faster speed.
C.
The grain freight train is traveling at a faster speed.
OD
There is not enough information to determine the speed of the trains.

Answer 1

Answer:

The coal freight train is traveling at a faster speed.

Step-by-step explanation:

The complete question is attached.

Both trains delivery can be represented using coordinates, where y represent the distance traveled and x represent the hours.

For the coal freight train, we can take two points. Let us use (1, 49) and (3, 147). Hence:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-49=\frac{147-49}{3-1} (x-1)\\\\y-49=49(x-1)\\\\y=49x$

For the grain freight train, we can take two points. Let us use (0, 0) and (3, 135). Hence:

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{135-0}{3-0} (x-0)\\\\y=45x$

Since the coal freight train has a slope (49) higher than the grain freight train (45), hence the coal freight train travels faster