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?

Question

29-10-2022
Mathematics

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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?

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RylynO105967 RylynO105967 · Answer 1 · 2022-10-29T23:38:36+02:00

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

=

[tex](x-\frac{20}{60})\text{ =(x-}\frac{1}{3})\text{ hours}[/tex]

The distance the marshall would have covered is.

[tex]15(x-\frac{1}{3})=(15x-5)\text{ miles}[/tex]

This distance is equal, so

[tex]\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-\frac{1}{3})\text{hours =(5-}\frac{1}{3}) \\ =4\frac{2}{3}\text{ hours} \end{gathered}[/tex]