SOLUTION: It took a crew 9 h 36 min to row 9 km upstream and back again. If the rate of flow of the stream was 7 km/h, what was the rowing speed of the crew in still water?

Question 1200265: It took a crew 9 h 36 min to row 9 km upstream and back again. If the rate of flow of the stream was 7 km/h, what was the rowing speed of the crew in still water?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

9 hrs 36 min = 9.6 hrs
since 36 min = 36/60 = 0.6 hrs

x = speed of the boat in still water
where x > 7

When going upstream, the boat is slowed down to a speed of x-7 km/hr.
When going downstream, the boat is sped up to a speed of x+7 km/hr.

Upstream:
distance = rate*time
9 = (x-7)*t1
t1 = 9/(x-7)
It takes 9/(x-7) hours to row upstream.

Downstream:
distance = rate*time
9 = (x+7)*t2
t2 = 9/(x+7)
It takes 9/(x+7) hours to row downstream.

The two time values (t1 and t2) must add to the total 9.6 hours mentioned earlier.

Multiply both sides by the LCD (x-7)(x+7) to clear out the fractions.

We have an equation in the form ax^2+bx+c = 0
a = 8
b = -15
c = -392
Plug those into the quadratic formula.

or

or

or
A negative speed value doesn't make sense, so we ignore
The only practical answer is

Answer: The speed of the boat in still water is 8 km/hr.

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