Question

A man jogs at a speed of 0.96 m/s. His dog waits 2.3 s and then takes off running at a speed of 3.4 m/s to catch the man. How far will they have each traveled when the dog catches up with the man

Answer 1

When the dog starts running, the man has jogged (0.96 * 2.3 = 2.208) meters.

We can set up an equation to solve for T

2.208 + 0.96T = 3.4T
2.208 = 2.44T
T = 0.904918

You can use either side of the previous equation to evaluate the distance traveled.

2.208 + 0.96 * 0.904918 = 3.076721 meters
3.4 * 0.904918 = 3.076721 meters

Answer 2

Answer:

The dog and the man meet 3.0767m later.

Step-by-step explanation:

The first thing to know is the speed formula. It is $v=\frac{x}{t}$ , where v is speed, x is distance and t is time. If you find x the formula would be $x=v\cdot t$

The first step is to obtain the distance equation for the man:

$x_{man}=v_{man}\cdot t=0.96\cdot t$

For the dog's distance equation, a little detail must be taken into account. The dog takes off running 2.3s after the man did. With that in mind, you must subtract 2.3 from t.

$x_{dog}=v_{dog}\cdot (t-2.3)=3.4\cdot (t-2.3)$

For finding the point where the dog catches up with the man you must match the equations of each one and then obtain find the t value. The procedure is shown:

$x_{man}=x_{dog}$

$0.96\cdot t=3.4\cdot (t-2.3)$

$0.96\cdot t=3.4\cdot t - 7.82$

$2.44\cdot t=7.82$

$t=\frac{7.82}{2.44}$

$t=3.2049s$

The previous result means that they meet in 3.2049s after the man started running. This value is used in the distance equation of the man.

$x_{man}=0.96\cdot t=(0.96)\cdot (3.2049)$

$x_{man}=3.0767m$

Finally, the dog and the man meet 3.0767m later.