Question56. A plane takes 1 and a half hour to fly from Los Angeles to San Francisco and 2 hours from San Francisco to Los Angeles. If the wind blows north on both trips at 24 mph , what is the speed of the plane in still air? A. 170 B. 110 C. 120 D. 150

Studdy Solution

STEP 1

1. The plane flies from Los Angeles to San Francisco in 1.5 hours.
2. The plane flies from San Francisco to Los Angeles in 2 hours.
3. The wind blows north at 24 mph on both trips.
4. We need to find the speed of the plane in still air.

STEP 2

1. Define variables for the speed of the plane in still air and the distance between the two cities.
2. Write equations for each trip considering the wind speed.
3. Solve the system of equations to find the speed of the plane in still air.

STEP 3

Define variables.
Let $v$ be the speed of the plane in still air (in mph). Let $d$ be the distance between Los Angeles and San Francisco (in miles).

STEP 4

Write equations for each trip considering the wind speed.
For the trip from Los Angeles to San Francisco (with the wind): $\frac{d}{v + 24} = 1.5$
For the trip from San Francisco to Los Angeles (against the wind): $\frac{d}{v - 24} = 2$

STEP 5

Solve the system of equations to find the speed of the plane in still air.
First, solve each equation for $d$ .
From the first equation: $d = 1.5(v + 24)$
From the second equation: $d = 2(v - 24)$
Set the two expressions for $d$ equal to each other: $1.5(v + 24) = 2(v - 24)$
Expand both sides: $1.5v + 36 = 2v - 48$
Rearrange to isolate $v$ : $36 + 48 = 2v - 1.5v$ $84 = 0.5v$
Solve for $v$ : $v = \frac{84}{0.5}$ $v = 168$
The speed of the plane in still air is $\boxed{168}$ .

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