Truck 1. Truck 2. Truck 3
Hors. Miles. Hours. Miles. Hours. Miles
3. 195. 1.5. 75. 0.5. 30
4. 260. 1.75. 87.5. 1.25. 75
4.5. 292.5. 2.5. 125. 3.5. 210
Three trucks travel the given distances in the specified amounts of time. Which statement is true.
A. None of the three trucks are traveling at the same rate of speed
B. All three trucks are traveling at the same rate of speed
C. Trucks 1 and 3 are traveling at the same rate of speed, but truck 2 is traveling more quickly
D. Trucks 1 and 2 are traveling at the same rate of speed, but Truck 3 is traveling more slowly
To determine which statement is true, we need to calculate the rate of speed (in miles per hour) for each truck.
For Truck 1:
Speed = Distance / Time
Speed = 195 miles / 1.5 hours
Speed ≈ 130 miles per hour
For Truck 2:
Speed = Distance / Time
Speed = 75 miles / 0.5 hours
Speed = 150 miles per hour
For Truck 3:
Speed = Distance / Time
Speed = 30 miles / 4 hours
Speed = 7.5 miles per hour
Based on the calculations, we can see that Trucks 1, 2, and 3 are not traveling at the same rate of speed. Therefore, the correct statement is:
A. None of the three trucks are traveling at the same rate of speed
To determine which statement is true, we need to compare the rates of speed for each truck. The rate of speed can be calculated by dividing the distance traveled by the amount of time taken.
For Truck 1:
Rate of Speed = Distance / Time = 195 miles / 1.5 hours = 130 miles per hour
For Truck 2:
Rate of Speed = Distance / Time = 75 miles / 0.5 hours = 150 miles per hour
For Truck 3:
Rate of Speed = Distance / Time = 30 miles / 0.5 hours = 60 miles per hour
Now let's compare the rates of speed:
Truck 1: 130 miles per hour
Truck 2: 150 miles per hour
Truck 3: 60 miles per hour
Since all three trucks have different rates of speed, we can eliminate option B.
Truck 2 has the highest rate of speed, so it cannot be true that Truck 2 is traveling more quickly than Trucks 1 and 3. Therefore, option C can be eliminated.
Trucks 1 and 2 have different rates of speed, so it cannot be true that they are traveling at the same rate. Therefore, option D can be eliminated.
Thus, the only remaining option is A. None of the three trucks are traveling at the same rate of speed.
To determine which statement is true, let's compare the speeds of the three trucks.
Truck 1:
Distance: 195 miles
Time: 1.5 hours
Speed = Distance / Time = 195 miles / 1.5 hours = 130 miles/hour
Truck 2:
Distance: 75 miles
Time: 0.5 hours
Speed = Distance / Time = 75 miles / 0.5 hours = 150 miles/hour
Truck 3:
Distance: 30 miles
Time: 0.5 hours
Speed = Distance / Time = 30 miles / 0.5 hours = 60 miles/hour
After calculating the speeds, we find that Truck 1 is traveling at 130 miles/hour, Truck 2 is traveling at 150 miles/hour, and Truck 3 is traveling at 60 miles/hour.
Therefore, statement C is true: Trucks 1 and 3 are traveling at the same rate of speed, but Truck 2 is traveling more quickly.