Lake Approximate Distance Around Lake (Miles)

Question

A 6
B 8
C 21
D 18
E 15

Part 1
Directions: Use the Information in the chart to solve each problem. Show your work by writing equations.

1.Margot hiked around Lake C each day. How many miles did she hike in 12 days? Draw a bar diagram to show how you solved the problem.

2. Keenan hiked 15 times as far as Margot. How far did Keenan hike? Use partial products to solve.

Answer 1

Part 1

Problem 1: Margot's Hiking Distance

Margot hiked around Lake C, which has an approximate distance of 21 miles around.

To find out how many miles she hiked in 12 days, we can use the following equation:

\[ \text{Total Distance} = \text{Distance Around Lake C} \times \text{Number of Days} \]

Substituting the values we have:

\[ \text{Total Distance} = 21 , \text{miles} \times 12 , \text{days} \]

To calculate \(21 \times 12\):

1. Break down the multiplication using partial products:
   • \(21 \times 12 = (20 + 1) \times 12\)
   • \(= 20 \times 12 + 1 \times 12\)
   • \(= 240 + 12\)
   • \(= 252\)

So, Margot hiked a total of 252 miles in 12 days.

Bar Diagram

          Margot's Hiking Distance

|-----------------------|-----------------------|
| Length of each hike   | Total Distance        |
|          21 miles     |         252 miles     |
|                       12 times                 |
|-----------------------|-----------------------|

Problem 2: Keenan's Hiking Distance

Keenan hiked 15 times as far as Margot. To find out how far Keenan hiked, we use the following equation:

\[ \text{Keenan's Distance} = \text{Margot's Distance} \times 15 \]

Using the distances:

\[ \text{Keenan's Distance} = 252 , \text{miles} \times 15 \]

Now, let's calculate \(252 \times 15\) using partial products:

1. Break down the multiplication:
   • \(252 \times 15 = 252 \times (10 + 5)\)
   • \(= 252 \times 10 + 252 \times 5\)
   • \(= 2520 + 1260\)

Now, add those two results together:

\[ 2520 + 1260 = 3780 \]

So, Keenan hiked a total of 3780 miles.