The average length of 6 ropes was 80 cm. The average length of 4 ropes of the ropes A, B, C and D was 15 cm more than the average length of the remaining 2 ropes E and F.
a) Find the average length of ropes E and F. Give your answer in metres.
b) If Rope E had been 18 cm shorter and Rope F had been 12 cm longer, they would have been of the same length. Find the actual length of Rope E.
Solution
Total of 6 ropes ----- 6 x 80cm = 480 cm
Average of A, B, C, D (4 ropes) is more than Average of E and F (2 ropes) by 15 cm.
This means each of the 4 ropes (A, B, C, D) has an average length that is 15 cm longer than the average of E and F.
Therefore, total length of A, B, C, D is longer than total length of E and F by
----- 4 x 15cm = 60 cm
a)
3 units ----- 480cm - 60cm = 420 cm
1 unit (E + F) ----- 420cm divided by 3 = 140 cm
Average ----- 140cm divided by 2 = 70 cm or 0.7 m
Answer: 0.7 m
b)
2 parts ----- 140 - 12 - 28 = 110
1 part ----- 110 divided by 2 = 55
E ----- 55 + 12 + 18 = 85
Answer: 85 cm
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