The track team is trying to reduce their time for a relay race. First they reduce their time by 2.1 minutes. Then they are able to reduce that time by 1/10. If their final time is 3.96 minutes, what was their beginning time?

6.5 minutes

Step-by-step explanation:

Let the initial time be X minutes.

No. of minutes of reduction of time = 2.1

Time left after reduction of 2.1 minutes = (X - 2.1)Minutes

Fraction of time reduce again 1/10 of time left = (1/10) * (X - 2.1)Minutes

Time left after reduction of (1/10) * (X - 2.1)Minutes

= (X - 2.1)Minutes - {(1/10) * (X - 2.1)Minutes}

=> (1-1/10)*(X - 2.1)Minutes

=> (9/10) * (X - 2.1)Minutes

Absolute value of time as given in question is 3.96 minutes

therefore, we have

(9/10) * (X - 2.1)Minutes = 3.96 minutes

=> (X - 2.1)Minutes = (10/9) * 3.96 minutes

=> X = 4.4 + 2.1 = 6.5

Therefore the beginning time was 6.5 minutes.

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629

im guessing (23,14). hope this : )