Question

Read the given problem statement and conclusion. Determine if the problem can be solved using the expression $\frac{3}{5}\times 4\frac{5}{3}$.
Problem: A cyclist covered $4\frac{5}{3}$ miles in the first $2$ hours. In the 3rd hour, he traveled $\frac{3}{5}$ times the distance he covered in the first two hours. Find the distance covered in the 3rd hour.

Conclusion: The distance traveled by the cyclist in the 3rd hour is less than 3 miles.

• A. Both options A and B are correct.
• B. The problem can be solved using the expression $\frac{3}{5}\times 4\frac{5}{3}$
• C. The conclusion to the given problem is correct.
• D. The given problem cannot be solved using the expression $\frac{3}{5}\times 4\frac{5}{3}$

Answer 1

The correct option is B The problem can be solved using the expression $\frac{3}{5}\times 4\frac{5}{3}$

Distance covered in the first $2h=4\frac{5}{3}mi$
Distance covered in the 3rd hour $=\frac{3}{5}$ times the distance covered in the first two hours.
$=\frac{3}{5}\times 4\frac{5}{3}$
So, this problem can be solved using the given expression. Hence, option A is correct.

Now, to verify the conclusion,
Let’s convert $4\frac{5}{3}$into an improper fraction.
$4\frac{5}{3}=4+\frac{5}{3}=\frac{4\times 3}{1\times 3}+\frac{5}{3}=\frac{12}{3}+\frac{5}{3}=\frac{17}{3}$
$\frac{3}{5}\times 4\frac{5}{3}=\frac{3}{5}\times \frac{17}{3}=\frac{51}{15}$
Write $\frac{51}{15}$ as a mixed fraction.

$\text{Mixed fraction}=\text{quotient}\times \frac{\text{reminder}}{\text{divisor}}=3\frac{6}{15}$
Therefore, $\frac{51}{15}=3\frac{6}{15}$, which is greater than $3$
The distance traveled by the cyclist in the 3rd hour is greater than 3 miles. Hence, the given conclusion is incorrect.