A jet leaves an airport traveling at a steady rate of 600 km/h. Another jet leaves the same airport 3/4 hr later taveling at 800 km/$ in the same direction. How long will it take the second jet to overtake the first.
RT = D (rate x time = distance)
800 = rate of 2nd jet
T = time of 2nd jet
800T = distance of 2nd jet
600 = rate of 1st jet
T + .75 = time of 1st jet (3/4h = .75h)
600(T + .75) = distance of 1st jet
Distances are equal
600(T + .75) = 800T
Solve for T
2 hours and 25 minutes
To find out how long it will take the second jet to overtake the first, we need to determine the time it takes for the distance covered by both jets to be the same.
Let's assume the time it takes for the second jet to overtake the first is 't' hours.
In that case, the first jet would have traveled for (t + 3/4) hours since it departed 3/4 hour earlier.
Distance covered by the first jet = Speed x Time
Distance covered by the second jet = Speed x Time
According to the given information:
Distance covered by the first jet = 600 km/h x (t + 3/4) hr
Distance covered by the second jet = 800 km/h x t hr
Since both jets cover the same distance when the second jet overtakes the first, we can equate the distances:
600 km/h x (t + 3/4) hr = 800 km/h x t hr
Now we can solve this equation to find the value of 't':
600t + 450 = 800t
Rearranging the equation:
200t = 450
Dividing both sides of the equation by 200:
t = 450 / 200
Simplifying:
t = 2.25 hours
Therefore, it will take the second jet 2.25 hours to overtake the first.
To determine how long it will take for the second jet to overtake the first jet, we need to calculate the time it will take for the distance between them to be equal.
Let's assume that it takes the second jet, which is traveling at 800 km/hr, time "x" to overtake the first jet.
In the time it takes the second jet to overtake the first jet, the first jet will have already traveled. The distance traveled by the first jet can be calculated using the formula: distance = speed × time.
Since the first jet is traveling at a steady rate of 600 km/hr and it has a head start of 3/4 hr, its travel time will be x + 3/4 hr.
Therefore, the distance traveled by the first jet can be represented as: distance = speed × time = 600 km/hr × (x + 3/4 hr).
The second jet, traveling at 800 km/hr, will need to cover the same distance as the first jet to overtake it. So, the distance traveled by the second jet can be represented as: distance = speed × time = 800 km/hr × x.
Now, we can equate the distances traveled by the two jets: 600 km/hr × (x + 3/4 hr) = 800 km/hr × x.
Simplifying this equation, we have: 600x + 450 = 800x.
To solve for x, we subtract 600x from both sides and divide both sides by 200: 450 = 200x.
Dividing 450 by 200, we find x = 2.25 hours.
Therefore, it will take the second jet 2.25 hours to overtake the first jet.