What are the answers to these 2?

Question

A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water AND the rate of the current.


and:


When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?


and can you show me HOW you got the answer please?

Answer 1

1) S = sailboat, R = river
20 miles/ 4hr = 5 mph = S - R
S = 5 + R
20 miles/3hr = S + R = 5 + 2R
20 = 15 + 6 R
R = 5/6 mph, so S = 5 5/6 mph

2)X = first digit, Y = second digit
X + Y = 11
Y = 11 - X
10X + Y + 9 = 10Y + X
9X - 9Y = -9 = 9X - 9(11 - X) = 18X - 99
18X = 90
X = 5, Y = 6

Answer 2

Ok I'll bite ..
Lets say the number looks like tihs: AB
Actually, its value is 10A + B
When you reverse the digits, you get a number that looks like this: BA, and its actual value is 10B + A
The new number is 9 more than the oritinal number
In other words, (1) 10B + A = 9 + 10 A + B
Also, the sum of the digits of the original number is 11
So (2) A + B = 11
Simplify equation (1) and you get 9B - 9A = 9
Solve the system, either by substitution or additon, whichever you prefer. I think I'll go with substitution this time, A = 11 - B
so 9B - 9(11 - B) = 9
9B - 99 + 9B = 9
18B - 99 = 9
B = (99 + 9)\18 = 6
B+A = 11 so A = 5
So the original number is 56 and the new number is 65

Answer 3

Speed of boat in still water = x
Water speed (current) = y While going downstream, 20 miles in 3 hours i.e.
20/(x+y) = 3 ....... x + y = 20/3
Upstream 20 miles in 4 hours .... 20/(x-y) = 4 ...... x - y = 5
ADD these two equations to solve for x and y .....
2x = 20/3 + 5 = 35/3 mph
x = 35/6 mph and y = 5/6 mph

Answer 4

1) speed of sailboat +current = 20mile/3 hour
= 6.67 mph

speed of sail boat - current = 20/4 hour
= 5 mph

speed of sail boat + current = 6.67
-
speed of sail boat - current = 5.0
==========================
2(current) =1.67
current = 0.83 mph

boat = 6.66 - 0.83 = 5.83 mph

2)sum of digits possiblities:

9+2=11
8+3=11
7+4=11
6+5=11

65 is 9 more tham 56. So the original number is 65

Answer 5

#1
downstream speed=(speed of boat in still water+speed of current).......say (x+y)

thus x+y=20/3..........(1)

upstream speed==(speed of boat in still water-speed of current).......say (x-y)

thus x-y=20/4=5......(2)

solving (1) and (2), we get

x=speed of boat in still water=35/6=5.83mph(approx) and
y=speed of current=5/6=0.83mph(approx)


#2
let the digits be x and y
original number is (10x+y)

when digits are reversed, number is (10y+x)
Now new number is 9 more............therefore
(10y+x)-(10x+y)=9
=>9y-9x=9
=>y-x=1..........(1)

also sum of digits are 11.......therfore
x+y=11............(2)

Solving for (1) and (2) we get,

y=6
x=5

thus original number is 10x+y=10*5+6=56........

Answer 6

let v=speed of boat in still water & c=speed of current
20miles/(v+c)mph=3hrs
20/(v-c)=4
20=3(v+c)
20/3=v+c
20=4(v-c)
5=v-c
20/3=v+c add
5+20/3=2v
15/3+20/3=2v
35/3=2v
v=35/6mph is the speed of the boat in still water.
5=v-c
20/3=v+c subtract
15/3-20/3=-2c
-5/6=-c
c=5/6 mph speed of current.
v=35/6mph is the speed of the boat in still water.

Answer 7

I don't know about the first question, but for the second one, I just used logic to find that the original number is 56 and the new number is 65.

Answer 8

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