Question

Translate to a system of equations and then solve: Charlie left his mother’s house traveling at an average speed of 36 miles per hour. His sister Sally left 15 minutes (1/4 hour) later traveling the same route at an average speed of 42 miles per hour. How long before Sally catches up to Charlie?

Short answer

It will take Sally 1.5 hours to catch up to Charlie

Step-by-step solution

Given Information 

Charlie left his mother’s house traveling at an average speed of 36 miles per hour. His sister Sally left 15 minutes (1/4 hour) later traveling the same route at an average speed of 42 miles per hour

Frame equations

Let 't' be the time taken by Charlie

Sally left 15 minutes (1/4 hour) late . so time taken by Sally is (t-1/4)

Charlie speed is 36 miles per hour. Sally speed is 42 miles per hour,

distance = speed * time

Distance travelled by Charlie is 36t

distance travelled by Sally is $42(t-\frac{1}{4})$

Solve for t

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

$$\begin{gathered} 36t=42\left(t-\frac{1}{4}\right) \\ 36t=42t-\frac{21}{2} \\ 36t-42t=42t-\frac{21}{2}-42t \\ \frac{-6t}{-6}=\frac{-\frac{21}{2}}{-6} \\ t=\frac{7}{4} \end{gathered}$$

Time taken for Sally =

$$\begin{gathered} t-\frac{1}{4} \\ \frac{7}{4}-\frac{1}{4}=\frac{6}{4}=1.5 \end{gathered}$$

It will take Sally 1.5 hours to catch up to Charlie