Answer:
The dog catches up with the man 6.1714m later.
Explanation:
The first thing to take into account is the speed formula. It is [tex]v=\frac{d}{t}[/tex], where v is speed, d is distance and t is time. From this formula, we can get the distance formula by finding d, it is [tex]d=v\cdot t[/tex]
Now, the distance equation for the man would be:
[tex]d_{man}=v_{man}\cdot t=1.6\cdot t[/tex]
The distance equation for the dog would be obtained by the same way with just a little detail. The dog takes off running 1.8s after the man did. So, in the equation we must subtract 1.8 from t.
[tex]d_{dog}=v_{dog}\cdot (t-1.8)=3\cdot (t-1.8)[/tex]
For a better understanding, at t=1.8 the dog must be in d=0. Let's verify:
[tex]d_{dog}=v_{dog}\cdot (1.8-1.8)=3\cdot (0)=0[/tex]
Now, for finding how far they have each traveled when the dog catches up with the man we must match the equations of each one.
[tex]d_{man}=d_{dog}[/tex]
[tex]1.6\cdot t=3\cdot (t-1.8)[/tex]
[tex]1.6\cdot t=3\cdot t-5.4[/tex]
[tex]1.4\cdot t=5.4[/tex]
[tex]t=\frac{5.4}{1.4}[/tex]
[tex]t=3.8571s[/tex]
The result obtained previously means that the dog catches up with the man 3.8571s after the man started running.
That value is used in the man's distance equation.
[tex]d_{man}=1.6\cdot t=1.6\cdot (3.8571)[/tex]
[tex]d_{man}=6.1714m[/tex]
Finally, the dog catches up with the man 6.1714m later.
