Q 113 - Intermediate Algebra

Question

College roommates John and David were driving home to the same town for the holidays. John drove $55$ mph, and David, who left an hour later, drove $60$ mph. How long will it take for David to catch up to John?

Step-by-Step Solution

Answer

$11$ hours will take for David to catch up to John.

Step 1 Given information are,

John drove $55$ mph, and David, who left an hour later, drove $60$ mph.

Both are traveling in the same distance.

Step 2 To find: The time taken for David to catch up to John.

Let $x$ represents the length of time for John.

$y$ represents the length of time for David.

Step 3 From the given information,

Let us draw a table.

Also, it is given that, John and David are traveling in the same direction.

So, $55x=60y$

Step 4 After one hours David travels in the same route.

Since David left later, his time will be less than one hour than John.

So, $y=x-1$.

Now substitute $y=x-1$ in the equation $55x=60y$.

$$\begin{gathered} 55x=60\left(x-1\right) \\ 55x=60x-60 \\ 60x-55x=60 \\ 5x=60 \\ x=\frac{60}{5} \\ x=12 \end{gathered}$$

Step 5 Find the value of y .

Substitute $x=12$ in the equation $y=x-1$.

$$\begin{gathered} y=12-1 \\ y=11 \end{gathered}$$