We are told that two trains, A and B, are traveling at a constant rate. We are asked to determine which train is traveling at a faster rate. First, let's calculate the rate of Train A.
Train A
The relationship between the time and distance of Train A is given to us in a table.
Time (hr)
2
3
4
5
6
Distance (mi)
50
75
100
125
150
The constant rate at which Train A is traveling is its speed. Let's recall the formula for speed.
Speed=Distance/Time
To find the speed of Train A, we can take any pair of times and distances from the table and plug it into the formula.
Time (hr)
2
3
4
5
6
Distance (mi)
50
75
100
125
150
Speed=Distance/Time
50/2= 25
75/3= 25
100/4= 25
125/5= 25
150/6= 25
We can see that the speed of Train A is 25 miles per hour. Now, let's calculate the speed of Train B.
Train B
Observing Train B's graph of distance and time, we can see that the line passes through the point (1,20).
This means that the train traveled 20 miles in 1 hour. Also, we know that the speed of Train B is constant. Therefore, we can say that the speed of Train B is 20 miles per hour.
Comparison
We found the rate at which each train is traveling.
