At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 45 mi/hr. Two hours later, a second truck leaves along the same route, traveling at 55 mi/hr. When will the second truck catch up to the first?
The first truck is 2 x 45 = 90 miles ahead when the second truck starts.
Once they are both moving, the distance between them decreases at a rate of 10 mi/hr. It will therefore take 90/10 = nine hours. The time when the second truck catches up is 9 hours after 11 AM, or 8:00 PM.
To find when the second truck catches up to the first truck, we need to determine the distance traveled by both trucks and compare them.
Let's start by calculating the distance traveled by the first truck. We know that it starts at 9:00 a.m. and travels west at a rate of 45 mi/hr. We can use the formula:
Distance = Rate × Time
The first truck travels for a total of (Time + 2) hours, because it leaves two hours earlier than the second truck. So the distance traveled by the first truck is:
Distance1 = 45 mi/hr × (Time + 2) hours
Now, let's calculate the distance traveled by the second truck. We know that it starts two hours later than the first truck and travels at a rate of 55 mi/hr. So the distance traveled by the second truck is:
Distance2 = 55 mi/hr × Time
To find when the second truck catches up to the first truck, we need to set the distances equal to each other and solve for Time:
Distance1 = Distance2
45 mi/hr × (Time + 2) hours = 55 mi/hr × Time
Now we can solve this equation:
45 (Time + 2) = 55 Time
45 Time + 90 = 55 Time
90 = 55 Time - 45 Time
90 = 10 Time
Time = 9
Therefore, the second truck will catch up to the first truck 9 hours after it starts, which is at 6:00 p.m.