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# I don’t understand

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Machine A can produce 160 cups of orange juice in an hour, while Machine B can produce 560 cups of orange juice in 2 1/3 hours.

a. Which machine operates at a faster rate?

b. If both machines operate together, how long will it take them to produce 1 800 cups of orange juice?

Aug 7, 2023

#1
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Part A:

Machine A can produce $$160 \times 2\frac{1}{3} = 373\frac{1}{3}$$ cups of orange juice in 2 1/3 hrs

So, we can conclude that machine B operates at a faster rate

Part B:

Well, Machine B produces $$560 \div \frac{7}{3} = 560\times \frac{3}{7} = 240$$ cups of orange juice per hour.

So, both combined can produce 400 cups of orange juice per hour, so for 1800 cups, it will take $$\frac{1800}{400} = 4.5$$ hours

Hope this helped, EJ

Aug 7, 2023
edited by Imcool  Aug 7, 2023
#2
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a. Rate =  cups / hrs

So

A =  160 / 1   = 160  cups per  hour

B =  560 / (2 1/3)  =  560 / ( 7/3)  =  560 (3/7) =  240 cups per hr

b.

1800 / [ 160 + 240] =  1800 /  400 =  18/4 = 9/2  =  4 .5 hrs

Aug 7, 2023