(1) To fill a water tank completely, tap A takes 7 minutes more time for tap than water. The time required for tap (A) to open both the taps together takes 160 minutes more time. To fill that tank completely, do not consume each tap differently. .
Answers
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the answer is 167 minutes .
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Answer:
28 minutes, 21 minutes
Step-by-step explanation:
Let the time taken by tap B to fill the tank is 'x' minutes.
∴ Part filled by tank B in 1 minute = (1/x).
Given that A takes 7 minutes more than tap B.
Then, the time take by tap A is 'x + 7' minutes.
∴ Part filled by tan A in 1 minute = (1/x + 7).
Part of the tank filled by (A + B) in 1-minute = (1/x) + (1/x + 7)
= [x + 7 + x]/[x(x + 7]
= [2x + 7]/[x² + 7x]
∴ Total time = [x² + 7x]/[2x + 7]
Given that Tap A takes 16 minutes more than the time taken by both.
=> x + 7 = {[x² + 7x]/[2x + 7]} + 16
=> (2x + 7)(x + 7) = (x² + 7x) + 16(2x + 7)
=> 2x² + 14x + 7x + 49 = x² + 7x + 32x + 112
=> 2x² + 21x + 49 = x² + 39x + 112
=> x² - 18x - 63 = 0
=> x² - 21x + 3x - 63 = 0
=> x(x - 21) + 3(x - 21) = 0
=> (x - 21)(x + 3) = 0
=> x = 21, -3{∴Cannot be negative}
=> x = 21.
Now:
=> x + 7
=> 28.
Therefore:
→ Time taken by tap A = 28 minutes.
→ Time taken by tap B = 21 minutes.
Hope it helps!