We need to use the distance formula, d = r × t, distance equals rate times time or, equivalently, t = d / r. But we need to use this to find the time for each direction separately. As background, the eastbound flight, from Albuquerque to Atlanta, benefits from the tradewinds, which blow west to east in the northern hemisphere as a consequence of (and lagging against) the earth's rotation around the polar axis. We are told only the distance and the relative amount by which eastward flight is faster than westward, 18%. We can use this by representing the westward speed as r (miles per hour) and the eastward speed as r + 0.18r = r(1 + 0.18) = 1.18 r. Now, using the distance equation in the (algebraically) equivalent form where we have solved for time, we can express the total flight time as d / r + d / (1.18r). To simplify this, we can factor out the d on top and the r on bottom, and we are left with 1 + 1 / 1.18. Multiplying the left-hand 1 by 1.18 / 1.18 and adding denominators, we get 2.18 / 1.18 = 218 / 118 = 109 / 59, which is in lowest terms since the numerator and denominator are relatively (actually, both) prime. Remembering the d/r, our expression so far is 109d/59r. Finally, substituting 1270 for d, we get 138430 / 59r, or 2346.27 / r. We might also represent this as (2.18 × 1270) / (1.18 r), which is "exact" but not completely simplified.
