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Question 238439: Mary has 200 knitted squares. Sue has 5000 knitted squares. Mary makes 20 knitted squares per hour. Sue makes 15 knitted squares per hour. Mary and Sue will start working (and continue to work every hour to add to their knitted square collections on the same day at the same hour. After the first hour, how many knitted squares will Mary have; how many knitted squares will Sue have? After the 2nd hour, 3rd hour? How many hours must they work until they both have the same amount of knitted squares?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mary has 200.
she knits 20 per hour.
after each hour, she has:
220, 240, 260, 280, 300, .....
sue has 5000.
she knits 15 per hoour.
after each hour, she has:
5000, 5015, 5030, 5045, 5060, etc.....
in order to make the same number of squares, the number of squares mary has must equal the number of squares that sue has.
let m = number of squares mary has.
let s = number of squares sue has.
mary starts at 200 and adds squares at the rate of 20 per hour.
sue starts at 5000 and adds squares at the rate of 15 per hour.
formuls for mary would be:
m = 200 + 20*h
formula for sue would be:
s = 5000 + 15*h
h is the number of hours they work.
if m = s, then:
200 + 20 * h = 5000 + 15 * h
solve for h.
subtract 15 * h from both sides of the eqution to get:
200 + 20 * h - 15 * h = 5000
combine like terms and simplify to get:
200 + 5 * h = 5000
subtract 200 from both sides of the equation to get:
5 * h = 5000 - 200
combine like terms and simplify to get:
5 * h = 4800
divide both sides of the equation by 5 to get:
h = 4800 / 5
simplify to get:
h = 960
it would take 960 hours for mary to make as many squares as sue.
200 + 960 * 200 = 19400
5000 + 960 * 15 = 19400
this makes sense because she is behind 4800 squares and she gains 5 squares per hour.
4800 / 5 = 960 which is exactly what the formula worked out to be.
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