Solve the problem.
-Natasha rides her bike (at a constant speed)for 3 hours, helped by a wind of 3 miles per hour. Pedaling at the same rate, the trip back against the wind takes 9 hours. Find find the total round trip distance she traveled.

Question

Quizplus · Accepted Answer

The total distance traveled is the sum of the distances for each leg of the trip. Let $x$ be Natasha's speed in miles per hour without wind. With the wind, her speed is $x + 3$ mph, and against the wind, it is $x - 3$ mph. The distance for each leg is speed times time. For the first leg, the distance is $3(x + 3)$ and for the return leg, it's $9(x - 3)$. Since the distances are equal, we set them equal to each other and solve for $x$: $3(x + 3) = 9(x - 3)$. Solving for $x$ gives us the speed without wind, but we're interested in the total distance, which is twice the distance of one leg (since it's a round trip and each leg is the same distance). Solving the equation directly for distance, we find that the total distance is 54 miles, considering the time and adjusted speeds for both legs of the trip.

Solve the Problem 272\frac { 27 } { 2 }227​ Miles C)27 Miles D)12 Miles

Solve the Problem $\frac { 27 } { 2 }$ Miles
C)27 Miles
D)12 Miles