Q. 358 - Intermediate Algebra

Question

In the following exercises,translate to a system of equations and solve.

Sheila and Lenore were driving to their grandmother's house.Lenore left one hour after sheila.Sheila drove at a rate of 45 mph,and lenore drove at a speed of 60 mph.How long it will take for Lenore catch up to sheila?

Step-by-Step Solution

Answer

3 hours to take for Lenore catch up to sheila

Step 1.Given information

Let x be the length of the time of sheila

Let y represents length of the time of Lenore

The following chart will help us organize the data

Name	Rate	Time	Distance D=r.t
Sheila	45	x	45x
Lenore	60	y	60y

To make the system of equations,you must recognize that sarah and her sister will drive the same distance

so, $45x=60y$

Since Lenore left her house after one hour,her time will be 1 hour less that sheila time,

so $$\begin{gathered} y=x-1 \\ x=y+1 \end{gathered}$$

Step 2.Find the time take for Lenore to catch up to sarah

Substitute $x=y+1$ in equation $45x=60y$ and solve for y.

$$\begin{gathered} 45x=60y \\ 45(y+1)=60y \\ 45y+45=60y \\ -15y=-45 \\ y=3 \end{gathered}$$

Substitute y=3 into $y=x-1$ and solve for x

$$\begin{gathered} y=x-1 \\ 3=x-1 \\ x=4 \end{gathered}$$

Step 3.Check

Substitute

Sheila:-

45x=45(4)

       =180

Lenore:-

60y=60(3)

       180

Yes, they will have to travelled the same distance  when they meet.

Therefore,3 hours to take for Lenore to catch up to sheila