An airplane flies 460 miles with the wind and 310 against the wind in the same length of time. If the speed of the wind is 30, what is the speed of the airplane still in the air?

Answer 1

1. An airplane flies 460 miles with the wind. Distance 1 = 460 miles
2. An airplane flies 310 against the wind in the same length of time. Distance 2 = 310 miles
3. If the speed of the wind is 30. Velocity of wind (Vw) = 30 miles per hour (mph)
4. Time with the wind equals time against the wind; T1 = T2

What are you solving for in the mathematical problem?

The speed of the airplane still in the air.

Information required to Solve the problem:

Speed = Distance divided by Time or v = d divided by t v = velocity, t = time

va = velocity of the airplane

vw = velocity of the wind

Time = distance divided by speed or time = distance divided by velocity

Step 1:

Express time with the wind.

Time with the wind is distance divided by speed

T1 = d1 divided by v1

T1 = d1 divided by va + vw

T1 = 460 divided by va + 30

Step 2:

Time against the wind is distance divided by speed

T2 = d2 divided by v2

T2 = d2 divided by va-vw

T2 = 310 divided by va -30

Step 3:

Equate the times and solve for va

Since T1 = T2

460 divided by va + 30 = 310 divided by va -30

Cross Multiply

460 (va -30) = 310 (va + 30)

460va -460 times 30 = 310va +310 times 30

460va - 13800 = 310va + 9300

460va -310va = 9300 + 13800

150va = 23100 divide 150 on both sides

va = 23100 divided by 150

va = 154

Solution to math problem:

The speed of the airplane still in the air is 154 mph (miles per hour)

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I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.