Question

If Machine A makes a yo-yo every five minutes and Machine B takes ten minutes to make a yo-yo, how many hours would it take them working together to make 20yo−yos?

Answer 1

If every 5 mins, A makes 1 yo-yo every 10 mins, B makes 1 yo-yo then every 10 mins, both machines produce 3 yo-yos every 10 mins (2 from machine A and 1 from machine B) Therefore, for 20 yo-yos, both machines would take 70 minutes( 1 hour and 10 mins). After 70 minutes, 21 yo-yos would be produced.

Answer 2

$\text{Answer: They need }1\frac{1}{9}\text{ hours working together to make 20 yo yos}$

Explanation:

Since we have given that

Time taken by Machine A to make a yo- yo = 5 minutes

Work done by Machine A in 1 minute is given by

$\frac{1}{5}$

Time taken by Machine B to make a yo - yo = 10 minutes  

Work done by Machine B in 1 minute is given by

$\frac{1}{10}$

Work done by both of them altogether is given by

$\frac{1}{5}+\frac{1}{10}=\frac{2+1}{10}=\frac{3}{10}$

Now, he can do,

$\frac{3}{10}\text{ work in 1 hour by both of them }$

We need to find the number of hours working together to make 20 yo-yos,

$\frac{10}{3}\times 20=\frac{200}{3}\ minutes=\frac{200}{3\times 60}\ hours=\frac{10}{9}\ hours=1\frac{1}{9}\ hours$

Hence,

$\text{ They need }1\frac{1}{9}\text{ hours working together to make 20 yo yos}$