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Home / Assignment Help / Which of the following best explains why deforestation increases the risk of floods in an area? a. Tree leaves catch and retain rain water. b. Trees block the free flow of water. c. Deforestation increases precipitation. d. Tree roots improve soil water retention.

# Which of the following best explains why deforestation increases the risk of floods in an area? a. Tree leaves catch and retain rain water. b. Trees block the free flow of water. c. Deforestation increases precipitation. d. Tree roots improve soil water retention.

Velocity of the boat relative to the stream = b

Velocity ot the boat downstream = b + 8

Velocity of the boat upstream = b – 8

v = d / t => t = d / v

Time downstream = 80 /  [b + 8]

Time upstream = 80 / [b – 8]

Total time 80 / [b + 8] + 80 / [b – 8] = 17/3 … [ I converted 5 h + 20 m to 1/

hours]

Now you have to solve

80 / [b + 8] + 80 / [b – 8] = 17/3

80[b – 8] + 80[b + 8] = [17/3](b+8)(b-8)

Divide by 80

b – 8 + b + 8 = [17/(80*3)] (b^2 – 64)

2b = [17/240]b^2 – 64*17/240

0.0708b^2 -2b – 4.53333 = 0

Use the quadratic formula to solve. You will obtain b = – 2.11 and b = 30.36

Only the positve result make sense. Then the answer is b = 30.36 mph.

Let’s verify that that result is coherent:

Downstream velocity = 30.36 + 8 = 38.36 mi / h
Downstream time = 80mi / 38.36 mi/h = 2.085 h

Upstream velocity = 30.36 – 8 = 22.36 mi / h
Upstream time = 80 mi / 22.36 mi/h = 3.578 h

Total time = 2.085 h + 3.578 h = 5.663 h, which is 5 h + 20 min; then, the result is correct. 