Question

Bus A travels according to the function y= 125/2


​
x, where y is the distance traveled in miles and x is time in hours.

Bus B travels according to the graph below, where the distance y is a function of time x.

Which bus travels faster? Include all necessary calculations in your final answer.

Answer 1

I can’t see the graph you mention — please upload it or give the coordinates (or read‑off points) from the graph. Meanwhile here is how to decide and the calculation you’ll need.

1. Bus A:
- y = (125/2) x so speed = slope = 125/2 = 62.5 miles per hour.

2. Bus B:
- From the distance–time graph, find two clear points on any linear segment, (x1,y1) and (x2,y2).
- Compute slope = speed = (y2 − y1) / (x2 − x1) in miles/hour.

3. Compare:
- If Bus B’s slope > 62.5, Bus B is faster (on that interval).
- If Bus B’s slope < 62.5, Bus A is faster.
- If equal, they travel at the same speed.

Example: if the graph passes through (0,0) and (2,150), Bus B’s speed = 150/2 = 75 mph, which is faster than Bus A (75 > 62.5).

Send the graph or two points from it and I’ll compute and state which bus is faster with the full calculations.