Bunuel wrote:

A transcontinental jet travels at a rate of x – 100 mph with a headwind and x + 100 mph with a tailwind between Wavetown and Urbanio, two cities 3,200 miles apart. If it takes the jet 2 hr 40 minutes longer to complete the trip with a headwind, then what is the jet’s rate flying with a tailwind?

(A) 500

(B) 540

(C) 600

(D) 720

(E) Cannot be determined by the information given.

Kudos for correct solution.

quick way is to plug the values,

Let take option C

therefore tailwind rate is = x+100 = 600

Now putting the values in \(speed= \frac{dist}{time}\) formula

we get \(600 = \frac{3200}{time}\)

or time = 5 hr 20 min

now calculating for headwind we have

since we have taken x+100 = 600 or x= 500

therefore headwind speed = x-100 = 500-100= 400

Putting the value in \(speed = \frac{distance}{time}\)

we get \(time = \frac{3200}{400} = 8 hour\) which exactly 2 hr 40 mins addition to tailwind. So ans is 600.

When putting the values in the equation it is better to choose from option C and then depending on the result we can go above C or below C.

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