Chapter 5: Q. 231 (page 646)

In the following exercises, translate to a system of equations and solve.
A small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Short Answer

Expert verified

The speed of the jet in still air and the speed of the wind are 240 mph and 28 mph respectively.

Step by step solution

Step 1. Given Information

The given data is that a small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind.

Step 2. Explanation

Let x be the rate of the jet with tailwind and y be the rate of headwind.

The jet fly with tailwind for 4 hours and the distance covered is 1072 miles and the actual rate of jet is $x + y$ and the distance covered can be expressed as $4 (x + y) = 1072 - - (1)$

The jet fly with headwind for 4 hours. So, the actual rate of the jet is $x - y$ and the distance covered is $4 (x - y) = 848 - - (2)$

Step 3. Calculation

Solve the equations (1) and (2) by adding both the equations.

$4 x + 4 y + 4 x - 4 y = 1072 + 848 8 x = 1920 x = 240$

Substitute the value of x in equation (1) to get the value of y.

$4 (240) + 4 y = 1072 4 y = 1072 - 960 4 y = 112 y = 28$

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In the following exercises, translate to a system of equations and solve.
A small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation

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In the following exercises, translate to a system of equations and solve. A small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Decision Maths

Applied Mathematics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, translate to a system of equations and solve.
A small jet can fly 1,072 miles in 4 hours with a tailwind but only 848 miles in 4 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.