Chapter 1.6, Problem 6P

To determine

To translate: each of the two given problem into an equation and also find the distance covered by Jan

Answer to Problem 6P

The distance traveled by Jan is $12\text{ miles}$

Explanation of Solution

Given Information:

The statements

(1) Brenda drove three times as far as Jan.

(2) Brenda drove 24 miles more than Jan

The given statements express the relation between distance covered by two people Brenda and Jan.

1. The first statement implies the distance traveled by Brenda is three times that of Jan

2. The second statement implies the sum of distance traveled by Jan along with 24 miles gives the distance traveled by Brenda.

It is expressed in the following figure.

  

Now, to convert these statements into suitable equation, one of the unknown distances has to be assigned a variable and the other distance is to be expressed in terms of the first variable.

Let the distance traveled by Jan be j .

(A) Based on the statement in (1), the distance traveled by Brenda is 3j .

(B) Now, as per statement (2), the equation connecting the distance traveled by Brenda and Jan can be written as,

  $j+24=3j$

Solving the above equation leads to the distance covered by Jan. The solution is,

  $\begin{array}{l}2j=24\\ j=12\end{array}$

This gives the distance traveled by Jan which is 12 miles.

The answer can be checked by seeing that Brenda has covered exactly 3 times the distance covered by Jan, 36 miles and it is 24 miles more than the distance covered by Jan.