Question

James can jog twice as fast as he can walk. He was able to jog the first 9 miles to his grandmother’s house, but then he tired and walked the remaining 1.5 miles. If the total trip took 2 hours, then what was his average jogging speed?

Answer 1

Let the speed of walking of James = x mile/hour

            speed of jogging = 2x mile/hour

9/2x + 1.5/x = 2

or, (9 + 3)/2x = 2

or, 12 = 4x

or, x = 3

Average speed of walking = 3 mile/hour

Average speed of jogging = 2 * 3 = 6 mile/hour

Answer 2

The average jogging speed of James is $\boxed{6\text{ miles per hour}}$.

Further explanation:

Given:

Total distance travelled by james while jogging is $9\text{ miles}$.

Total distance travelled by James while walking is $1.5\text{ miles}$.

Total time taken by James is $2\text{ hours}$.

Formula used:

The time required to cover a distance of $d$ at a speed of $s$ is calculated as follows:

$\boxed{t=\dfrac{d}{s}}$

Calculation:

Consider the walking speed of James as $x$ miles per hour and the jogging speed as $2x$ miles per hour.

Time taken to cover the distance of $9\text{miles}$ at a speed of $2x$ miles per hour can be calculated as follows:

$\boxed{t_{1}=\dfrac{9}{2x}}$

Here, $t_{1}$ is time taken to cover the distance $9\text{miles}$.

Time taken to cover the distance of $1.5\text{miles}$ at a speed of $x$ miles per hour can be calculated as follows:

$\boxed{t_{2}=\dfrac{1.5}{x}}$  

Here, $t_{2}$ is time taken to cover the distance $1.5\text{ miles}$.

Total time taken to cover the total distance is $2\text{ hour}$.

The above expression is represented in equation form as,

$\begin{aligned}\dfrac{9}{2x}+\dfrac{1.5}{x}&=2\\ \dfrac{9+(2\times1.5)}{2x}&=2\\9+3&=4x\\x&=\dfrac{12}{4}\\x&=3\end{aligned}$

Therefore the speed of walking is $3\text{ miles per hour}$.

The speed of jogging is twice the speed of walking so, the speed of jogging is calculated as follows:

$\boxed{2\times 3=6}$

Therefore, the average jogging speed of James is $6$ miles per hour.

Thus, the average jogging speed of james is $\boxed{6\text{ miles per hour}}$.

Learn more:

1. Solution of linear equation: //brainly.com/question/1682776

2. Magnitude of the speed brainly.com/question/1597065

Answer details:

Grade: Middle school.

Subject: Mathematics.

Chapter: Speed and distance.

Keywords: Speed , acceleration , distance cover, 9 mi, 1.5 mi. jogging speed, walking speed, James, Average, time, grandmother’s house.