Question

Machine X can make 3 widgets in 1.5 hours. Working together but independently, Machines X and Y can make 7.5 widgets in 2.5 hours. If both machines started working at the same time and each produced 3.5 widgets, and if Machine X finished at noon, at what time did Machine Y finish? '

Answer 1

At 01:45 pm machine Y will finish the work.

Explanation:

Machine X can make 3 widgets in 1.5 hours.

So per hour production of machine X =
`(3)/(1.5)=2` widgets

Let rate of production of machine Y = y gadgets per hour

Now it is given that machines X and Y can make 7.5 widgets in 2.5 hours.

So per hour rate of production by both the machines =
`(7.5)/(2.5)=3` widgets per hour

Then production rate of machine X + production rate of machine Y = Rate of production by both the machines X and Y

2 + y = 3

y = 3 - 2

y = 1 widget per hour

Both the machines started working at the same time and they produced 3.5 widgets.

Then time taken by machine X with the rate 2 widgets per hour =
`(3.5)/(2)=1.75` hours

If machine X finished at noon then the time at which both the machines started working = 12 : 00 - 1 hour 45 minutes

= 10 : 15 am

Time taken by machine Y with the rate 1 widget per hour =
`(3.5)/(1)=3.5` hours

So the time by which machine Y will finish = 10:15 am + 3.5 hours

= 01:45 pm

Therefore, at 01:45 pm machine Y will finish the work.