Question

A bus travels at a constant speed. The following table shows the distance the bus travels (in kilometers) over a period of time (in hours).
distance (d) 42 252 378
time (t) 0.5 3 4.5
Use complete sentences to describe the relationship represented in the table.
Write an equation using variables that represents the relationship shown in the table.
Use your equation to find how far the bus travels in 6 hours.

Answer 1

Answer:

315 km

Step-by-step explanation:

If the bus travels at constant speed, then the slope of the distance versus time graph can be calculated by using any two points from this table.

Let's use the points (0.5, 42) and (4.5, 378):

as we move from the first point to the second, t increases by 4 and y increases by 336.  Thus, the slope of this graph is

m = rise / run = 336 km  /  4 hr  =  84 km/hr

then distance traveled = speed times time, or

distance traveled = (84 km/hr)t, where t is the elapsed time.

In 6 hours the bus would travel

                                 ( 84 km/hr )(6 hr) = 504 km, or approx. 315 mi

Answer 2

Answer:

The slope of the line is 84. It means the bus travels at a constant speed of 84 km per hour. The equation d=84t represents the relationship shown in the table. The distance covered by the bus after 6 hours is 504 km.

Step-by-step explanation:

It is given that bus travels at a constant speed.

If a line passing through two points then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

From the given table it is clear that the line passing through (0.5,42) and (3,252). The slope of the line is

$m=\frac{252-42}{3-0.5}=84$

The slope of the line is 84. It means the bus travels at a constant speed of 84 km per hour.

The equation of line is

$y-y_1=m(x-x_1)$

$y-42=84(x-0.5)$

$y-42=84x-42$

$y=84x$

Substitute x=t and y=d in the above equation.

$d=84t$

The equation d=84t represents the relationship shown in the table.

The distance covered by the bus after 6 hours is

$d=84(6)=504$

Therefore the distance covered by the bus after 6 hours is 504 km.