Wyatt hiked for 4.7 hours at a rate of 2.9 miles per hour. He determined that he hiked 13.63 miles. Which best explains the reasonableness of Wyatt’s answer?

Question

There are two digits to the left of the decimal in the factors and two digits to the left of the decimal in the product, so Wyatt’s answer is reasonable.
There are two digits to the right of the decimal in the factors and two digits to the right of the decimal in the product, so Wyatt’s answer is reasonable.
Wyatt’s answer is reasonable because 4 times 2 is 8, and 8 is close to 13.63.
Wyatt’s answer is reasonable because 5 times 3 is 15, and 15 is close to 13.63.

Answer 1

To determine the reasonableness of Wyatt's answer, we can look at the multiplication involved in calculating the distance hiked. Wyatt's calculation was:

\[ \text{Distance} = \text{Time} \times \text{Rate} \] \[ \text{Distance} = 4.7 , \text{hours} \times 2.9 , \text{miles/hour} \]

To estimate:

1. Round 4.7 to 5 (a simpler number).
2. Round 2.9 to 3 (also a simpler number).

Now, perform the multiplication:

\[ 5 \times 3 = 15 \]

Now, we can see that 15 is greater than Wyatt's answer of 13.63 but it's close enough to suggest that his calculation is reasonable.

Considering the options, the correct choice among the provided explanations is:

Wyatt’s answer is reasonable because 5 times 3 is 15, and 15 is close to 13.63.