Question 152973: 1. The sum of two numbers is 70. Their difference is 34. What are the numbers?
2. It takes a ferryboat 2 hours to travel 30 miles going downstream and 3 hours for the return trip upstream. What is the ferryboat's speed in still water?
3. Yolanda is twice as old as Tyrone. Six years from now the sum of their ages will be 27 years. How old are Yolanda and Tyrone now?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 1. The sum of two numbers is 70. Their difference is 34. What are the numbers?
:
x + y = 70
x - y = 34
--------------adding eliminates y, find x
2x = 104
x = 52
then
y = 70 - 52
y = 18
:
Check 52 - 18 = 34
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2. It takes a ferryboat 2 hours to travel 30 miles going downstream and 3 hours for the return trip upstream. What is the ferryboat's speed in still water?
:
Let x = boat speed in still water
Let y = current speed
then
speed down stream = (x+y)
speed up stream = (x-y)
:
Write a distance equation for each trip; dist = time * speed
2(x+y) = 30
3(x-y) = 30
Simplify, divide the 1st equation by 2 and the 2nd equation by 3, results:
x + y = 15
x - y = 10
-----------adding eliminates y, find x
2x = 25
x = 12.5 speed of boat in still water
:
Check solution by finding the current:
12.5 - y = 10
-y = 10 - 12.5
-y = -2.5
y = 2.5 mph speed of the current
:
2(12.5 + 2.5) = 30; confirms our solution
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3. Yolanda is twice as old as Tyrone.
y = 2T
:
Six years from now the sum of their ages will be 27 years.
(Y + 6) + (T + 6) = 27
Y + T + 12 = 27
Y + T = 27 - 12
y + T = 15
:
How old are Yolanda and Tyrone now?
:
Substitute 2T for Y in the above equation
2T + T = 15
T = 15/3
T = 5 yrs old, then obviously; Y = 10 yrs old
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