A rare whale fossil was uncovered under layers of sediment. When the excavator took measurements, she found the tail to be as long as its head plus a quarter of the length of the body. When the archaeologist came in, he measured the length of the body. He found it to be ¾ of the total length. They made arguments about how such a fish would swim in the water. To make proper predictions they measured the head size, and found it to be 4 inches long. What is the total length of this whale?
Answer:
A rare whale fossil was uncovered under layers of sediment. When the excavator took measurements, she found the tail to be as long as its head plus a quarter of the length of the body. When the archaeologist came in, he measured the length of the body. He found it to be ¾ of the total length. They made arguments about how such a fish would swim in the water. To make proper predictions they measured the head size, and found it to be 4 inches long. What is the total length of this whale?
Given : tail to be as long as its head plus a quarter of the length of the body
length of the body be ¾ of the total length.
Head 4 inches long
To Find : total length of this whale
Solution:
Head = 4 inch
Body = B inch
Tail = Head + (1/4) Body
= 4 + (1/4)B
= 4 + B/4 inches
Total Length = Head + Body + Tail
= 4 + B + 4 + B/4
= 8 + 5B/4
Body = (3/4) Total Length
=> B = (3/4)(8 + 5B/4)
=> 4B = 3( 32 + 5B)/4
=> 16B = 96 + 15B
=> B = 96
Total Length = 8 + 5B/4 = 8 + 5 * 96/4
= 8 + 5 * 24
= 8 + 120
= 128 inches
Head = 4 inches
Body = 96 inches
Tail = 28 inches
Total Length = 128 inches
total length of this whale 128 inches
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