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Help with Word Problems?
My teacher assigned a lot of word problems for homework due soon, and I am having a hard time figuring out how to do them.
There's different sections and I pulled some from random sections. If anyone could explain how to do any of them, that would be appreciated!
Thanks!
- Peter can build a deck in 10 hours. Paul can build a deck in 12 hours. How long would it take Peter and Paul working together to build a deck while Mary watches?
- A boat can move at a speed of 5 km/h in still water. The boat travels 42 km downstream in the same time it takes to travel 12 km up stream. What is the speed of the stream?
- y varies inversely as the square of x, and y =6 when x = 3. Find y when x =2 ( ME : Is y = 4?)
- What is the minimum product of 2 numbers whose difference is 14? What are the numbers that give this product?
2 Answers
- icemanLv 71 decade agoFavorite Answer
1) 1/10 + 1/12 = 1/t
11/60 = 1/t
t = 60/11 hrs
≈ 5.45 hrs or 5 hrs 27 minutes 16 seconds
2) d = vt
t = d/v
42/(5 + s) = 12/(5 - s)
7/(5 + s) = 2/(5 - s)
35 - 7s = 10 + 2s
9s = 25
s = 25/9 km/hr
≈ 2.78 km/hr
3) y = k/x^2
6 = k/9 => k = 54
y = 54/2 = 27
4) let the numbers be a and (a - 14)
a(a - 14)
= a^2 - 14a => set the derivative to 0
=> 2a - 14 = 0
2a = 14
a = 7
7 - 14 = - 7
the numbers are 7 and -7
- Anonymous1 decade ago
1) Peter Builds 1/10th of the deck in 1 hour
Paul builds 1/12th of the deck in 1 hour
together they build 1/10 + 1/12 if the deck in 1 hour
so they build 6/60 + 5/60th of the deck in 1 hour
that is..11/60th of the deck in one hour
so they take 60/11 ~ 5.45 hrs = 5 hrs 27 minutes
2)let the time taken for the boat to travel 42 km downstream or 12 km upstream be x
& let the speed of the stream be y
So,
42/x - y = 5 km/hr....(1)
12/x + y = 5 km/hr....(2)
Adding them we get,
54/x = 10
54 = 10x
54/10 = x
x = (27/5) hrs
Substitute x = 27/5 in equation (2)
12/(27/5) + y = 5 km/hr
y = 5 - 12/(27/5) km/hr
y = 45/9 - 20/9 km/hr
y = 25/9 km/hr
Speed of stream = 25/9 km/hr
