Question

start from 200 feet away, a person on a tractor rides towards a barn and then passes it. The rider is traveling at a constant rate of 8 feet per second. The distance between the tractor and the barn is given by the equation
d = |200 - 8t|. At what time is the tractor 20 feet away from the barn?

Answer 1

To find the time when the tractor is 20 feet away from the barn, we need to set the distance between the tractor and the barn equal to 20 feet and solve for t.

The equation for the distance between the tractor and the barn is given by d = |200 - 8t|, where d is the distance and t is the time in seconds.

Setting this equation equal to 20 feet:

20 = |200 - 8t|

Next, we can write two separate equations based on the absolute value sign:

1) 20 = 200 - 8t
2) 20 = -(200 - 8t)

Simplifying each equation:

1) 8t = 200 - 20
8t = 180
t = 180/8
t = 22.5 seconds

2) 20 = -200 + 8t
8t = 200 + 20
8t = 220
t = 220/8
t = 27.5 seconds

Therefore, the tractor is 20 feet away from the barn at 22.5 seconds and 27.5 seconds.