Question

Sammy had 30 minutes to do a three problem quiz. She spent 10 1/3 minutes on problem 1 and 5 4/5 minutes on problem 2. How much time did she have time for problem 3? Write your answer as a mixed number.

Answer 1

The time spent on problem 3 is $13\frac{13}{15} \text{ minutes }$

Solution:

Given that Sammy had 30 minutes to do a three problem quiz

To find: Remaining time left for problem 3

From given question,

Total time = 30 minutes

Time spent on problem 1 = $10\frac{1}{3} \text{ minutes }$

$\rightarrow 10\frac{1}{3} = \frac{3 \times 10 + 1}{3} = \frac{31}{3} \text{ minutes }$

Time spent on problem 2 = $5\frac{4}{5} \text{ minutes }$

$\rightarrow 5\frac{4}{5} = \frac{5 \times 5 + 4}{5} = \frac{29}{5} \text{ minutes }$

Therefore,

Time spent on problem 3 = total time - (time on problem 1 + time on problem 2)

$\text{ Time spent on problem 3 } = 30 - (\frac{31}{3} + \frac{29}{5})\\\\\rightarrow 30 - \frac{31 \times 5 + 29 \times 3}{3 \times 5}\\\\\rightarrow 30 - \frac{242}{15}\\\\\rightarrow \frac{30 \times 15 - 242}{15}\\\\\rightarrow \frac{208}{15} = 13\frac{13}{15}$

Thus time spent on problem 3 is $13\frac{13}{15} \text{ minutes }$