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Question

Hi,

Need help for these 2 questions

  1. There were 330 green and blue marbles in a bag. 1/2 of the green marbles and 3/4 of the blue marbles were then taken out by Lisa. In the end, there were 90 green and blue marbles left in the bag. How many of the marbles in the bag were blue at first ?
  2.  A tank measuring 80cm by 50cm by 60cm was empty at first. Water from a tap started to fill the tank at a rate of 1.5 litres per min. when the tank was 5/8 full, a crack appeared at the base of the container. Water began to leak from the crack at a rate of 500cm3 per minute. What was the total time taken for the whole tank to be completely filled with water ?

Thanks in advanced.

 

Answer

1)
2G + 4B = 330

After removed 1G and 3 B of marbles
1G + 1B = 90
Multiply 2 to the above equation,
2G + 2B = 180

2G + 4b – (2G + 2B) = 330-180
2B = 150
B = 75

At first Blues = 4B = 300 ###

2) Total volume of Tank = 80 x 50 x 60 = 240, 000cm3
5/8 of 240,000cm3 = 150,000 cm3
Time taken to reach 5/8 of tank = 150,000/1500 = 100 mins

Remaining volume = 3/8 of 240,000 = 90,000 cm3
Effective fill rate of the remaining volumes = 1500 – 500 = 1000 cm3/min
Time taken to fill 3/8 of tank = 90,000/1000 = 90 mins

Total time taken is 100 + 90 = 190 mins or 3 hrs and 10 mins ###

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