At noon a private plane left Austin for Los Angeles, 2100 km away, flying at 500km/h. One hour later a jet left Los Angeles for Austin at 700 km/h. At what time did they pass each other?
Let t be the time after the first jet leaves for LA, and x be the location of a plane, measured from LA.
2100 - x = 500 t
x = 700 (t -1) = 700 t - 700
Substitute 2100 - 500 t for x in the second equation and solve for t.
2100 - 500 t = 700 t - 700
2800 = 1200 t
t = 7/3 hours = 2 hours & 20 minutes
To find out at what time the private plane and the jet pass each other, we can determine the time it takes for each of them to cover their respective distances. Let's break down the problem step by step:
1. Firstly, we need to determine the time it takes for the private plane to travel 2100 km at a speed of 500 km/h. We can use the formula:
time = distance / speed
Therefore, the time taken by the private plane is: time = 2100 km / 500 km/h = 4.2 hours.
2. The jet leaves Los Angeles one hour later than the private plane. So, we deduct this one hour from the total time taken by the private plane. Therefore, the time left for the jet to meet the private plane is: 4.2 hours - 1 hour = 3.2 hours.
3. Now, we need to determine how far the jet will travel in 3.2 hours at a speed of 700 km/h. We can again use the formula:
distance = speed * time
Therefore, the distance covered by the jet is: distance = 700 km/h * 3.2 hours = 2240 km.
4. As we already know that the total distance between Austin and Los Angeles is 2100 km, it is not possible for the jet and the private plane to pass each other before the jet reaches Austin. So, we can conclude that they meet when the jet arrives in Austin.
Therefore, the private plane and the jet pass each other at the time when the jet arrives in Austin. How long it takes for the jet to reach Austin depends on its speed. However, since we already calculated the time as 3.2 hours, we can use that to estimate the passing time.
If the private plane left at noon, and we add the 3.2 hours to noon, we can conclude that the jet and the private plane pass each other at approximately 3:12 PM.