A jet leaves the Charlotte, North Carolina, airport traveling at an average rate of 564 km/h. Another jet leaves the airport one half hour later traveling at 744km/h in the same direction. Use an equation to find how long the second jet will take to overtake the first.
at time t hr, the first plane goes 564t km
the second jet flies for 1/2 hour less, but at 744 km/h, so it has gone 744(t-.5)
When they have both gone the same distance,
744(t-.5) = 564t
744t - 372 = 564t
180t = 372
t = 2 hr 4 min
To solve this problem, we can use the formula:
Distance = Speed × Time
Let's assume the time taken for the second jet to overtake the first jet is 't' hours.
By the time the second jet starts, the first jet has already been flying for half an hour, which means it has covered a distance of:
Distance of first jet = Speed of first jet × Time of first jet
= 564 km/h × (t + 0.5) hours
The second jet travels at a faster speed and catches up with the first jet. So, the distance traveled by the second jet is equal to the distance covered by the first jet. Therefore, we can set up the equation:
Distance of second jet = Distance of first jet
= 744 km/h × t hours
Substituting the values in the equation, we have:
744 km/h × t = 564 km/h × (t + 0.5)
Now, we can solve this equation to find the value of 't'.
744t = 564t + 282
180t = 282
t = 282/180
t ≈ 1.57 hours
Therefore, the second jet will take approximately 1.57 hours to overtake the first jet.
To find the time it will take for the second jet to overtake the first jet, we need to set up an equation based on their relative speed and the time difference when the second jet starts.
Let's assume that the time it takes for the second jet to overtake the first jet is 't' hours. By the time the second jet catches up, the first jet would have been flying for (t + 0.5) hours, as it departs half an hour earlier.
Now, we know that the distance covered by both jets will be the same when the second jet overtakes the first jet. Hence, we can set up the equation:
Distance covered by the first jet = Distance covered by the second jet
The distance covered by an object can be calculated by multiplying its speed by the time it has been traveling. Therefore:
564 * (t + 0.5) = 744 * t
Now, we can solve this equation to find the value of 't'.
Let's solve it step by step:
564 * (t + 0.5) = 744 * t
Distribute:
564t + 282 = 744t
Rearrange the equation:
744t - 564t = 282
180t = 282
Divide both sides by 180:
t = 282 / 180
Simplify:
t ≈ 1.5667
Therefore, it will take approximately 1.5667 hours (or about 1 hour and 34 minutes) for the second jet to overtake the first jet.