Need Help With Only 3 PRoblems out of 45!! Here they are?

Question

1. Hookes Law. The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 67 cm when the weight is 4 kg. What is the distance when the weight is 8kg?

2. The speed of a stream is 3mph, a boat travels 3 miles upstream in the same time it takes to gtravel 9 miles downstream. What is the speed of the boat in still water?

3. Janet, an experienced clerk can fill a certain order in 9 hours, Jim, A new clerk, can fill the same order in 10 hours. Working togehter how long will it take them to fill the order.

I am helping my 16 yr old son with Algebra, all foreign to me, these are the 3 i dont know if the answers are correct, can you help?

Answer 1

1. Hookes Law. The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 67 cm when the weight is 4 kg. What is the distance when the weight is 8kg?

Answer:

The distance is twice as much = 134 cm

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Answer 2

1. Hooke's Law is
F = - kx, or F/x = - k
Using this equation to set up a proportion,
4/67 = 8/x
Solving for x,
x = 8*67/4

2. d = rt, t = d/r
r = s - 3 upstream, and
r = s + 3 downstream
3 / (s - 3) = 9 / (s + 3)
Inverting, we get
(s - 3) / 3 = (s + 3) / 9
Multiplying by 9,
3s - 9 = s + 3
Adding 9,
3s = s + 12
Subtracting s,
2s = 12
Dividing by 2,
s = 6 mph

3.
The combined rate,
R = (1 order / 9 hr + 1 order / 10 hr)
R = (1/9 + 1/10)orders/hr
Adding,
R = ((10 + 9)/90)orders/hr
Inverting, we have
1/R = 90 hours / 19 orders
1/R = 4.7368 hours per order