6
algebra

A plane flies 600 miles with a tailwind in 2 hours. The return trip against the wind takes 3 hours. What is the wind speed?

A

40 mph

B

50 mph

C

60 mph

D

75 mph

Correct Answer: B

Choice B is the correct answer. Let pp = plane speed in still air and ww = wind speed.

System: Distance = Speed × Time {(p+w)2=600(pw)3=600\begin{cases} (p + w) \cdot 2 = 600 \\ (p - w) \cdot 3 = 600 \end{cases}

Step 1: Simplify: {p+w=300pw=200\begin{cases} p + w = 300 \\ p - w = 200 \end{cases}

Step 2: Add equations: 2p=5002p = 500p=250p = 250

Step 3: Find ww: 250+w=300250 + w = 300w=50w = 50

Solution: Wind speed is 50 mph

Verification: With wind: (250+50)×2=600(250 + 50) \times 2 = 600 ✓, Against: (25050)×3=600(250 - 50) \times 3 = 600

💡 Strategic Tip: Wind/current helps in one direction, opposes in the other.

Choice A is incorrect because with w=40w = 40: plane speed would be 260, and return trip would be 220×3=660 eq600220 \times 3 = 660 \ eq 600.

Choice C is incorrect because with w=60w = 60: plane speed would be 240, and return trip would be 180×3=540 eq600180 \times 3 = 540 \ eq 600.

Choice D is incorrect because with w=75w = 75: plane speed would be 225, and return trip would be 150×3=450 eq600150 \times 3 = 450 \ eq 600.