Question

4a. Snail A moved 6 feet in 7 hours. Snail B moved 7 feet in 8 hours. Both snails moved at constant speeds. Which snail went faster? Solve this problem in two different ways, explaining in detail why you can solve the problem the way you do. In particular, if you use fractions in your explanation, be sure to explain how the fractions are relevant.

A student might say that snail B moved faster than snail A because the numbers for snail B are greater (in other words,
7 > 6 and 8 > 7) Even if the conclusion is correct, is the student’s reasoning valid? Explain why or why not.

Answer 1

Method 1:

Snail A:

6 Feet = 7 Hours

So,

1 Foot = 7/6 = 1.17 Hours

Snail B:

7 Feet = 8 Hours

So,

1 Foot = 8/7 = 1.14 Hours.

We note Snail A has taken 1.17 Hours to move 1 Foot.

Snail B has taken 1.14 Hours to move 1 Foot.

Since Snail B has taken less time, Snail B went faster.

Method 2:

Snail A:

7 Hours = 6 Feet

So,

1 Hour = 6/7 = 0.86 Feet

Snail B:

8 Hours = 7 Feet

So,

1 Hour = 7/8 = 0.875 Feet.

We note Snail A went 0.86 Feet in 1 Hour.

Snail B went 0.875 Feet in 1 Hour.

Since Snail B has moved more distance in 1 Hour, Snail B went faster.

The student's reasoning is not valid because all the three numbers: distance moved, time taken and speed are to be considered.