Question

after robbing a bank in dodge city a robber gallops off at 12mi/h. 10 minutes later the marshall leaves to pursue the robber at 15 mi/h. how long (in hours) does it take the marshall to catch up to the robber?

Answer 1

The marshall takes 40 minutes to catch up to the robber.

Step-by-step explanation:

The first step is to convert the units of the given speeds to miles per minute, since the time is given in minutes. The robber's speed is 12 mi/h, which is equal to 0.2 mi/min. The marshall's speed is 15 mi/h, which is equal to 0.25 mi/min.

Next, we need to find out how far the robber has traveled in the 10 minutes that he started before the marshall. Since the robber's speed is 0.2 mi/min, he has covered a distance of 0.2 mi/min * 10 min = 2 miles.

Now, we can set up an equation to represent the situation.

Let 't' represent the time it takes for the marshall to catch up to the robber. The distance the marshall travels is the same as the distance the robber has already covered, plus the distance covered by both the robber and the marshall during the time 't'.

So we have the equation: 0.2 mi/min * t + 2 miles = 0.25 mi/min * t. Solving this equation will give us the time 't' that it takes for the marshall to catch up to the robber.

Simplifying the equation, we have: 0.2t + 2 = 0.25t.

Subtracting 0.2t from both sides, we get: 2 = 0.25t - 0.2t = 0.05t.

Dividing both sides by 0.05, we get: t = 2 / 0.05 = 40 minutes.

Therefore, it takes the marshall 40 minutes to catch up to the robber.