Question

The position "d" of a bicyclist (measured in kilometers) is a linear function of time "t" (measured in minutes). At time t=6 minutes, the position is d=5 km. If the bicyclists travels at 2 km for every 5 minutes, find the position of the bicyclist at t=8 minutes.

Answer 1

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Answer 2

Answer:

Position of the bicyclists is 5.8 km.

Step-by-step explanation:

Let the equation of a linear function representing this situation is d = mt + c

Where m = slope of the line representing the function or rate of change in distance

Now rate of change of distance of velocity of the bicyclists m = $\frac{2}{5}=0.40$ km per minutes

when we plot distance and time at x and y axis  

At time t = 0 distance traveled by the bicyclist = 0

At time t = 6 minutes distance traveled d = 5 km

So at this point coordinates of the bicyclist will be (6, 5).

Similarly at t = 8 minutes coordinates will be (8, y)

Now we know slope m = $\frac{y-y'}{x-x'}$

Now we plug in the values in the formula of slope.

$\frac{2}{5}=\frac{y-5}{8-6}$

2×2 = 5(y - 5)

4 = 5y - 25

5y = 4 + 25 = 29

y = $\frac{29}{5}=5.8$ km

Therefore, at t = 8 minutes position of the bicyclist is 5.8 km.