Question

After robbing a bank in Dodge City a robber gallops off at 14 mi/h. 20 minutes later, the marshalls leaves to pursue the robber at 15 mi/h. How long (in hours) does it take the marshalls to catch up to the robber?

Answer 1

After robbing a bank in Dodge City a robber gallops off at 14 mi/h. 20 minutes later, the marshalls leaves to pursue the robber at 15 mi/h. How long (in hours) does it take the marshalls to catch up to the robber?

SOLUTION

Let it take x hours for the marshall to catch up with the robber since the robber started galloping.

In x hours, the robber would have covered 14 x miles

Now, the time for the marshall to catch the robber would be x - 20 minutes

=

`(x-(20)/(60))\text{ =(x-}(1)/(3))\text{ hours}`

The distance the marshall would have covered is.

`15(x-(1)/(3))=(15x-5)\text{ miles}`

This distance is equal, so

`\begin{gathered} 15x-5=14x \\ 15x-14x=5 \\ x=5\text{hours for the robber.} \\ The\text{ time it took the marshall to catch up with the robber is. } \\ (x-(1)/(3))\text{hours =(5-}(1)/(3)) \\ =4(2)/(3)\text{ hours} \end{gathered}`