Question

Translate to a system of equations and then solve: Mitchell left Detroit on the interstate driving south towards Orlando at a speed of 60 miles per hour. Clark left Detroit 1 hour later traveling at a speed of 75 miles per hour, following the same route as Mitchell. How long will it take Clark to catch Mitchell?

Short answer

It will take Clark 4 hours to catch Mitchell.

Step-by-step solution

Given Information 

Mitchell left Detroit on the interstate driving south towards Orlando at a speed of 60 miles per hour. Clark left Detroit 1 hour later traveling at a speed of 75 miles per hour,

assume variables 

Let 't' be the time taken by Clark

Michel left 1 hour before Clark . so time taken by Michel is (t-1)

Mitchell speed is 60 miles per hour. Clark speed is 75 miles per hour,

distance = speed * time

Distance travelled by Clark is 60t

distance travelled by Michel is 75(t-1)

solve for t

Distance travelled is same . So we set the distance equal and solve for t

$$\begin{gathered} 75(t-1)=60t \\ 75t-75=60t \\ subtract60tfrombothsides \\ 15t-75=0 \\ 15t=75 \\ Divideby15 \\ t=5 \end{gathered}$$

It will take Clark 4 hours to catch Mitchell.