Machine X can pack 3 crates of bottles and Machine Y can pack 4 crates of bottles within the same time. In half an hour, Machine X packs 24 crates. How many crates can 12 Machine Y s pack in 1 hour?
machine X can pack 48 crates per hour
since ratio of machine X : machine Y = 3 : 4
48 : machine Y = 3 : 4
3 machine Y = 192
machine Y can pack 64 crates per hour
(note 48:64 = 3:4)
so 12 machine Y's can pack 12(64) or 768 crates in 1 hour.
To solve this problem, we can start by calculating the rate at which Machine X packs crates. We know that Machine X can pack 24 crates in half an hour. Therefore, we can calculate its packing rate as:
Rate of Machine X = Number of crates packed / Time taken
Rate of Machine X = 24 crates / 0.5 hours
Rate of Machine X = 48 crates/hour
Now, we are asked to find out how many crates 12 Machine Ys can pack in 1 hour. We know that Machine Y packs 4 crates in the same time Machine X packs 3 crates.
Ratio of packing rates of Machine Y to Machine X = 4 crates / 3 crates
Ratio of packing rates = 4/3
Since we have 12 Machine Ys, we need to multiply the ratio of packing rates by the number of Machine Ys:
Total packing rate of 12 Machine Ys = Ratio of packing rates * 12
Total packing rate of 12 Machine Ys = (4/3) * 12
Total packing rate of 12 Machine Ys = 16 crates/hour
Therefore, 12 Machine Ys can pack 16 crates in 1 hour.