Another method is by puting the values of X As 500,540,600,720

First put the value of x as 500
Speeds are 400 and 600
time taken to travel 3200 is 8 hrs and 5 hrs 20 mins.
Difference in time is 2 hrs 40 min as given in the problem
so speed with tailwind is x+100 = 500+100 = 6

This will definately save time.

if the 500 does not work go with the choice 600 as it is easy to eliminate this choice first

Pranab01's solution, by plugging in answers, is the best way. But I wanted to point out why the algebra is a bad idea.

ALGEBRAIC METHOD:

If you decide to solve using algebra, you'd make a couple of equations using the rate formula: RT = D

(x + 100)t = 3200
and
(x - 100)(t + 2 2/3) = 3200

If you ever have two equations in which two variables are multiplied, and then a bit has been added or subtracted and they're multiplied again, this will turn into a quadratic equation. And not a nice one. Quadratics can be solved of course, but hidden quadratics like this usually can't be solved very quickly because there will be like 15 steps. So if you ever see any equation like this, go straight to the answer choices! It's guaranteed to be easier.

PLUG IN ANSWERS METHOD:

If you're going to plug in, as pranab01 did, don't just start with A. Usually you want to start with one of the middle answers so that if it's too large, you know to pick a smaller answer. It's also a good idea to try to pick whichever numbers will be easiest to deal with. Since C, 600, fulfills both categories, I'd start with C, and it's probably not a coincidence that C is the correct answer. For details on the plug-in method see pranab01's response.

Let's start with a "word equation"

(time with headwind) = (time with tailwind) + 2 hours 40 minutes

2 hours 40 minutes = 2 2/3 hours = 8/3 hours
Time = distance/speed

Plug the given values into the word equation to get: 3200/(x – 100) = 3200/(x + 100) + 8/3
Multiply both sides of the equation by 3 to get: 9600/(x – 100) = 9600/(x + 100) + 8
Multiply both sides of the equation by (x – 100) to get: 9600 = 9600(x – 100)/(x + 100) + 8(x – 100)
Multiply both sides of the equation by (x + 100) to get: 9600(x + 100) = 9600(x – 100) + 8(x – 100)(x + 100)
Expand and simplify: 9,600x + 960,000 = 9,600x – 960,000 + 8x² – 80,000
Subtract 9,600x from both sides: 960,000 = –960,000 + 8x² – 80,000
Divide both sides of the equation by 8 to get: 120,000 = –120,000 + x² – 10,000
Simplify right side: 120,000 = x² – 130,000
Add 130,000 to both sides: 250,000 = x²

Solve: x = 500 or x = -500
Since the speed cannot be negative, we know that x = 500

What is the jet’s rate flying with a tailwind?
x + 100 mph = speed with a tailwind
So, the speed with a tailwind = 500 + 100 = 600

Answer: C

Cheers,
Brent

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