Question

after robbing a bank in dodge city, a robber gallops off at 13 mi/h. 30 minutes later, the marshall leaves to pursue the robber at 15 mi/h. how long (in minutes) after the marshall takes off does it take the marshall to catch up to the robber?

Explanation:

Define variables and given values

Using the Uniform Motion Problems knowledge point
Let \(t\) be the time in hours after the marshall takes off.
The robber's speed is \(v_r = 13\text{ mi/h}\).
The marshall's speed is \(v_m = 15\text{ mi/h}\).
The robber has a head start of \(30\text{ minutes} = 0.5\text{ hours}\).

Set up the distance equation

Using the Uniform Motion Problems knowledge point

$$
LATEXBLOCK0
$$

Solve for time in hours

Using the Uniform Motion Problems knowledge point

$$
LATEXBLOCK1
$$

Convert the time to minutes

Using the Uniform Motion Problems knowledge point

$$
LATEXBLOCK2
$$

Answer:

After robbing a bank in Dodge City, a robber gallops off at 13 mi/h. 30 minutes later, the marshall leaves to pursue the robber at 15 mi/h. How long (in minutes) after the marshall takes off does it take the marshall to catch up to the robber?

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