Richard needs to fly from san diego to halifax, nova scotia and back in order to give an important talk about mathematics. on th

Question

1 month ago

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Richard needs to fly from san diego to halifax, nova scotia and back in order to give an important talk about mathematics. on th

e way to halifax, he will get a speed boost from the wind which blows at 50 miles per hour (mph). on the way back, the plane must, unfortunately, fight this wind speed. if the talk lasts 2 hours, and if the distance between the two cities is 3000 miles, how fast must the plane fly in mph if the entire trip is to take 13 hours?

Physics

2 answers:

kicyunya [3.2K] · Answer 1 · 2026-03-19T08:07:34+03:00

Response:

550 mph

Clarification:

Let the plane's speed be represented by p. Under wind assistance, the plane travels at $p+50$ mph in relation to the ground. Therefore, traveling to Halifax takes $\dfrac{3000}{p+50}$ hours. Conversely, the return trip requires $\dfrac{3000}{p-50}$ hours. Adding these to the 2 hours for the talk gives a total of 13 hours: \[\dfrac{3000}{p+50} + 2 + \dfrac{3000}{p-50}=13.\] After subtracting 2 and multiplying both sides by $(p+50)(p-50)$, we arrive at: \[3000(p-50)+3000(p+50)=11(p^2-2500)\]Which simplifies to $11p^2-6000p-27500=0$. Factoring this gives $(p-550)(11p+50) =0 $, leading us to the solution $p=\boxed{550} \text{ mph}$.

Alternatively, trial and error with the main time equation can be effective. The two fractions will be roughly equal, contributing a total of 11 hours. Testing values close to $500$ for p quickly leads to the correct answer without complicated calculations.