With the wind, a jet can fly 2500 km in 2 hours and 30 minutes. Against the wind, it can fly only 2000 km in the same time. Find the rate of the jet if the rate of the jet if the rate of the wind is 100 km/hr. Please Show All Work!
Not sure what you exactly want but here is what you will need to get your answers:
V1 - Velocity of the jet
V2 - Velocity of Wind
So 2500km/(V1+V2) = 2.5hrs ----- (1)
2000km/(V1-V2) = 2.5hrs ----- (2)
Solving for the above 2 equations:
2500V1 -2500V2 = 2000V1 + 2000V2
500V1 = 4500V2
or V1 = 9V2
Putting this in (1)
10V2 = 1000
V2 = 100km/hr (Wind)
V1 = 900km/hr (Jet)
That's the answer
To find the rate of the jet, we can first find the speed of the jet with no wind by subtracting the rate of the wind from the speed of the jet. Let's say the speed of the jet is represented by "j" and the rate of the wind is "w", which is given as 100 km/hr.
So, the speed of the jet with no wind is j - w, and the distance traveled against the wind can be represented as speed multiplied by time, which is 2000 km. Similarly, the speed of the jet with the wind is j + w, and the distance traveled with the wind is 2500 km.
Given that the time taken is 2 hours and 30 minutes, we need to convert this time into hours. Since there are 60 minutes in an hour, 30 minutes is equal to 30/60 = 0.5 hour. Therefore, the total time is 2 + 0.5 = 2.5 hours.
Now we can set up two equations based on the information given:
Against the wind: (j - w) * 2.5 = 2000
With the wind: (j + w) * 2.5 = 2500
Expanding these equations, we have:
2.5j - 2.5w = 2000
2.5j + 2.5w = 2500
Adding these two equations, the w term cancels out:
5j = 4500
Dividing both sides by 5, we get:
j = 900
Therefore, the speed of the jet is 900 km/hr.