Question

Sarah left Minneapolis heading east on the interstate at a speed of $60$mph. Her sister followed her on the same route, leaving two hours later and driving at a rate of $70$mph. How long will it take for Sarah’s sister to catch up to Sarah?

Short answer

$12$ hours will take for Sarah’s sister to catch up to Sarah.

Step-by-step solution

Given information is,

Sarah travels towards east at the speed of $60$mph.

After two hours, her sister follows her in the same route at the speed of $70$ mph.

To find:

The time taken for Sarah’s sister to catch up to Sarah.

Let$x$represents the length of the time of Sarah.

$y$ represents the length of the time of Sarah's sister.

From the given information,

Let us draw a table.

Since Sarah and her sister travels in the same distance,

$60x=70y$.

It is given that,

her sister travels in the same route after $2$hours from the Sarah's time.

So, $$\begin{gathered} y=x-2 \\ x=y+2 \end{gathered}$$

Now we are going to find out the unknown values by using the substitution method.

Substitute $x=y+2$in the equation $60x=70y$.

$$\begin{gathered} 60\left(y+2\right)=70y \\ 60y+120=70y \\ 70y-60y=120 \\ 10y=120 \\ y=\frac{120}{10} \\ y=12 \end{gathered}$$

Now find the value of x.

Substitute $y=12$in the equation $x=y+2$.

$$\begin{gathered} x=12+2 \\ x=14 \end{gathered}$$