This graph shows the relationship between the time Brandon has been on a bike ride, in minutes, and his distance from home in miles.

Question

Let’s say Brandon is 30 km from home. Do you know for sure how long it has been since he left home?
x
y
0
10
20
30
40
50
60
70
80
90
100
0
30
60
90
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Distance from home (km)
Elapsed Time (min)

I know for sure that it
has been 180 minutes
since he left home.

I do not know for sure how
long it has been since he
left home because it could
have been 60 minutes or
180 minutes.

I know for sure that it
has been 60 minutes
since he left home.

Answer 1

To determine how long it has been since Brandon left home based on the given information, let's analyze the scenario.

1. Distance from Home: Brandon is 30 km from home.
2. Unit Conversion: Since the y-axis indicates distance in kilometers (km) and we generally analyze distances in miles (mi) on such graphs, we will need to consider how many kilometers correspond to a distance from home in the context of the graph.

From the graph, it appears that you have a clear measurement of time elapsed against the distance from home. However, the relationship or slope of the graph (which may indicate speed or positional change over time) isn't provided in the description.

Conclusion:

Since he is 30 km from home on the graph, if we assume the graph implies that he could be on any trajectory, then it is ambiguous.

• He could have reached that distance in a shorter time (e.g., 60 minutes) if he was riding quickly, or it could take longer if he slowed down.

Thus, you cannot conclude definitively how long it has been since he left home based solely on him being 30 km away without additional information about the graph's slope or the route he took.

So, the correct statement would be:

"I do not know for sure how long it has been since he left home because it could have been 60 minutes or 180 minutes."