SOLUTION: A jet leaves Charlotte, North Carolina, airport traveling at an average rate of 564km/h. Another jet leaves the airport one half hour later traveling at 744km/h in the same direct

Question 537782: A jet leaves Charlotte, North Carolina, airport traveling at an average rate of 564km/h. Another jet leaves the airport one half hour later traveling at 744km/h in the same direction. How long will the second jet take to overtake the first?
Found 2 solutions by lmeeks54, Alan3354:
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
This is a twist on a classic distance (d), rate (r), and time (t) problem that links how far something goes in a certain amount of time.
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The basic formula is:
d = r * t
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This can be rewritten to solve for either of the other two quantities:
r = d / t
t = d / r
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In the basic problems, usually two of the three quantities are given and you solve for the missing quantity. In more complex problems, the trick is in figuring out what you are solving for. Just remember, eventually all these type problems eventually reduce down to a simple problem forcing you to solve for d, r, or t.
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In this case, two jets seems to complicate your problem definition. In the end, it will still be about one jet covering some distance at a given speed in some amount of time. Therefore, for this problem, the individual speeds of the two jets are less important than the difference in speeds between them.
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This is an important point: that is the one speed you need to enter the d = r * t formiula. Although two jets are flying, only one jet is doing the relative motion between them: the faster jet is catching up to the one ahead.
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Let x = the speed of the slowest jet in front
Let y = the speed of the faster jet catching up
Let r = the speed differential, which is y - x
... r = 744 km/h - 564 km/h
... r = 180 km/h
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The problem asks us to solve for how long till the faster jet catches the slower jet. It wants us to solve for t. Therefore, it presumes it is has given us enough information to calculate for d and r before solving for t.
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We just solved for r above, r = 180 km/h
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Likewise, we need to figure out d. It turns out that is just as simple for you: we know the fast jet starts out 30 minutes behind the slower jet. So the distance starts out at how far the slower jet traveled in that half hour to get ahead of the faster jet before it took off.
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We need a, the slower jet's speed for this:
recall, a = 564 km/h
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We'll use d = r * t for this calculation
d = 564 km/hr * 0.5 hrs
d = 564/2
d = 282 km
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So, we go back to the original problem. We now know the rate for that problem (180 km/h) and the distance we just figured out (282 km). Now we can go back into t = d / r to find the time for the faster jet to cover 282 km at a closing speed of 180 km/hr.
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t = 282 km/180 km/hr
t = 1.5667 hrs, or 94.0 mins
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The answer is 94 minutes; however, it is important to check your work. Do that by going back to the two jets' individual speeds and see far each gets.
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The 1st jet travels 30 mins (the head start) + 94 mins (time for 2nd jet to catch up @ 564 km/hr. Reminder we have time in minutes but the rate in km/hr so convert the time to hours. 30 + 94 = 124 mins = 2.067 hrs
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d = r * t
d = 564 km/hr * 2.067 hrs
d = 1,165.6 km
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The 2nd jet travels 94 mins (1.5667 hrs) @ 744 km/hr
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d = r * t
d = 744 km/hr * 1.5667 hrs
d = 1,165.6 km
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The work checks
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Cheers,
Lee
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A jet leaves Charlotte, North Carolina, airport traveling at an average rate of 564km/h. Another jet leaves the airport one half hour later traveling at 744km/h in the same direction. How long will the second jet take to overtake the first?
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The 1st plane is 282 km away when the 2nd leaves (564 * 0.5)
The 2nd plane gains on the 1st at 180 km/hr (744 - 564)
282/180 = 1.56667 hours to overtake
= 1 hr 34 minutes

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