Chapter 4: Q. 358 (page 480)

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?

Short Answer

Expert verified

3 hours to take for Lenore catch up to sheila

Step by step solution

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, $45 x = 60 y$

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

so $y = x - 1 x = y + 1$

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

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

$45 x = 60 y 45 (y + 1) = 60 y 45 y + 45 = 60 y - 15 y = - 45 y = 3$

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

$y = x - 1 3 = x - 1 x = 4$

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

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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?

Short Answer

Step by step solution

Step 1.Given information

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

Step 3.Check

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Most popular questions from this chapter

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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?

Short Answer

Step by step solution

Step 1.Given information

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

Step 3.Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Mechanics Maths

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

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?