SOLUTION: josie can type 100 words in the same time that it take jane to type 75 word. if jane's typing rate is 8 words per minute less than that of josie's, find jane's typing rate

Question 1037381: josie can type 100 words in the same time that it take jane to type 75 word. if jane's typing rate is 8 words per minute less than that of josie's, find jane's typing rate
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a = the typing rate of josie
let b = the typing rate of jane
let x = the time it takes for each of them to finish typing.
this means that josie takes x minutes to type 100 words.
this means that jane takes x minutes to type 75 words.

the general formula is rate * time = quantity.

for josie, this equation becomes a * x = 100
for jane, this equation becomes b * x = 75

solve both equations for x and you get:

x = 100/a
x = 75/b

this means that 100/a = 75/b
cross multiply to get 100b = 75a
solve for b to get b = 75a/100 which simplifies to b = 3/4 * a

you are given that b = a - 8.
replace b with a-8 in this equation to get a-8 = 3/4 * a
add 8 to both sides of this equation and subtract 3/4 * a from both sides of this equation to get a - 3/4 * a = 8
simplify to get 1/4 * a = 8
multiply both sides of this equation by 4 to get a = 32.

since b = a-8, you get:

a = 32
b = 24

since b = jane's typing rate, your answer is that ....

jane's typing rate is 24 words per minute.

you can confirm the answer is correct since they both took the same time.

rate * time = quantity

for josie, this means 32 * time = 100.
for jane, this means 24 * time = 75

solve for time in each equation and you get:

for josie, time = 100 / 32 = 25 / 8.
for jane, time = 75 / 24 = 25 / 8.

the time is the same, confirming the solution is correct.

there was another way to solve this as well.

same setup.

ax = 100
bx = 75

subtract the second equation from the first to get ax - bx = 25
factor out the x to get (a-b)x = 25
solve for x to get x = 25/(a-b)

you are given that b = a-8.
replace b in the equation to get x = 25/(a - (a-8))
simplify to get x = 25/8.

now that you know the time, you can solve for a and b.

a * 25/8 = 100
a * 25 = 8*100
a = 8*100/25 = 8*4 = 32

b * 25/8 = 75
b * 25 = 8*75
b = 8*75/25 = 8*3 = 24

you get the same answer either way.

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