Chapter ISG, Problem 6.1.2.6P

To determine

To define variables and write system of equations

Answer to Problem 6.1.2.6P

Time taken by C to walk to school is 34 minutes.

Explanation of Solution

Given information:

Total time spend by C= 2 hours 20 minutes.

Calculation:

Let time taken by bicycle= $x$ minutes

And time taken by walking= $y$ minutes

Number of days bicycle rode=2

And, number of day C walked=3

Total time taken=2 hours 20 minutes,

Converting into minutes,

Time taken=140 minutes

According to question,

Time taken by bicycle+ time taken by walking= Total time spent

  $2x+3y=140$  -(1)

Also, when C walked to school, she leave 15 minutes earlier, meaning that bicycle is 15 minutes faster.

Putting into equation,

  $y-x=15$  -(2)

Solving the equation,

Taking (2),

  $\begin{array}{l}y=x+15\\ \end{array}$  -(3)

Put in (1)

  $2x+3(x+15)=140$

Solving,

  $\begin{array}{l}2x+3x+45=140\\ 5x=95\end{array}$

Dividing equation by 5,

  $x=19$

Put value of x in (3)

  $y=19+15$

So,

  $y=34$

Graph:

Blue line represents: 2x + 3y =140

Orange line represents: y - x =15