Question

Khalid and Jesse took different overnight trains. The graph shows the relationship between the total distance Khalid traveled and the time in hours. The distance Jesse traveled after x hours is given by the equation y = 150x. Who, if anyone, traveled at a faster speed? Use the drop-down menus to explain your answer.

Khalid’s rate is ____ miles per hour. Jesse’s rate is ____ miles per hour. So, ____ train traveled at a faster speed.

Answer 1

Khalid’s rate is 140 mi/h. Jesse’s rate is 150 miles per hour

So, Jesse’s train traveled at a faster speed

Explanation:

Here, we want to compare speeds

For Jesse’s train, the speed is 150 mi/h

we got this from the fact that the equation of a straight line is represented as;

y = mx + b

where m which is the slope represents the rate of change

m here is 150

For Khalid’s;

we can get his own rate from the graph

This can be obtained using the slope

We can simply have this as ;

m = (y2-y1)/(x2-x1)

Let us have two points

(4,560) and (0,0)

Thus;

m = 560/4 = 140 mi/h

Hence;

Khalid’s rate is 140 mi/h. Jesse’s rate is 150 miles per hour

So, Jesse’s train traveled at a faster speed