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.
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I backsolved. I was taking too long to find the equations.

Start with Answer C, 500

Difference in time should be 2 hours 40 minutes = 2\(\frac{2}{3}\) = \(\frac{8}{3}\) hours

1. Find tailwind time from \(D/r\)

TW time is \(\frac{3200}{600}\) = \(\frac{32}{6}\) = \(\frac{16}{3}\) hours

2. Find headwind rate in order to find headwind time

Tailwind rate is 500 = x + 100, x = 400
Headwind rate is x - 100 = 300

3. Find headwind time

HW time is \(\frac{3200}{400}\) = \(\frac{32}{4}\) = 8 hours

4. Difference in time?

(8 -\(\frac{16}{3}\))=(\(\frac{24- 18}{3}\)) = \(\frac{8}{3}\) hours. Correct.

Answer C

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