Answer:
Step-by-step explanation:
Which cyclist lives closest to the park?
I'll rewrite both equations as y = mx + b so that they are more clearly understood.
A(x)= - 9.2x + 36.8
B(x)= - 13.8x + 41.4
The negative slopes represent the fact that both boys are headed toward the park from their homes, so as time increases, their distance from the park decreases. The y-intercept represents their starting points from the park (at time = 0, they are still at home, doing homework).
Distance from home: A: 36.8 miles; B: 41.4 miles. Boy A lives closest to the park.
Who will be the first to arrive at the park?
The slopes are their speeds. Boy B cycles faster, but has to cover a greater distance. A(x) and B(x) are 0 when they reach the park, Find the time, x, for each by setting that distance to 0.
A(x)= - 9.2x + 36.8
0 = - 9.2x + 36.8
9.2x = 36.8
x = 4 hours
B(x)= - 13.8x + 41.4
0 = - 13.8x + 41.4
13.8x = 41.4
x = 3 hours
Boy B arrives first.
How much earlier will that cyclist arrive?
From above, Boy B arrives one hour before Boy A. He uses that time flirting with a classmate while waiting.
Is there a time when both cyclists are the same distance from the orchard?
This is asking is there a time, x, in which both equations are wequal to each other:
A(x)= b(x) ?
A(x)=36.8 - 9.2x
B(x)= 41.4 - 13.8x
36.8 - 9.2x = 41.4 - 13.8x
4.6x = 4.6
x = 1 hour
At one hour they are both the same distance from the park.
