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Question

Just need help on these last problem and I m done with my homework! I m having problem making an equation for them.

1) Jack, Kay, and Lynn deliver advertising flyers in a small town. If each person works alone, it takes jack 4 hours to deliver the flyers and it takes lynn 1 hour longer than it takes kay. Working together, they can deliver all the flyers in 40% of the time kay working alone. How long does it take Kay to deliver all the flyers alone?

2) Kiran drove from tortula to cactus a distance of 250 mi. She increased her speed by 10mi/h for the 360 mi trip to dry junction. If the total trip took 11 hours what was her speed from tortula to cactus?

Answer 1

1)
let kay takes x hours working alone

Jack alone takes 4 hours

Lynn alone takes (x + 1) hours

Kay can do in 1 hr ---------- 1/x part
Jack can do in i hr ---------- 1/4 part
Lynn can do in 1 hr --------- 1/(x + 1)

altogether can do in 1 hr ----- 1/4 + 1/x +1/(x + 1) part
= x(x + 1)+ 4(x+1) + 4x/(4x(x + 1) part
=(x^2 + x + 4x + 4 + 4x)/(4x(x + 1)
=(x^2 +9x + 4)/4x(x + 1)
altogether can do 1 job = 4x(x + 1)/( x^2 + 9x + 4) hrs

4x^2 + 4x /(x^2 + 9x + 4) = 0.4 x
divide by 4x
x + 1/(x^2 + 9x + 4) = 0.1

multiply by 10
10x+ 10 = x^2 + 9x + 4
x^2 - x - 6 = 0
x^2 - 3x +2 x - 6 = 0
x(x - 3) + 2(x - 3) = 0
(x - 3)(x + 2) = 0
x= 3 ignoring negative value
so it takes 3 hours for Kay to do it alone

2)
let her speed from tortula to cactus = x mi/hr
time taken for this trip = 250/x hrs

her speed for dry junction = x + 10 mi/h
time taken for this trip = 360/(x + 10) hr

total time taken = 250/x + 360/(x + 10)
= 250(x + 10) + 360x/(x(x + 10)
= 250x + 2500 + 360x/(x^2 + 10x
= 610x + 2500/(x^2 + 10x)
610x + 2500/(x^2 + 10x) = 11
11x^2 + 110x = 610x + 2500
11x^2 - 500 - 2500 = 0
11x^2 - 550 + 50x - 2500 = 0
11x(x - 50) + 50(x - 50) = 0
(x - 50)(11x + 50)
x = 50 ignoring negative value
her speed from tortula to cactus = 50 mi/hr

Answer 2

number one is interesting.

It takes Jack 4 hours to deliver the flyers
let t be the time it takes Kay to deliver the flyers, then t + 1 is the time it takes Lynn to deliver the flyers

find the rates of all three:
in one hour, jack can deliver 1/4 of the flyers
Kay can deliver 1/t of the flyers
Lynn can deliver 1/(t + 1) of the flyers

we know that it takes Kay t hours to deliver all the flyers, then .4t is the time it takes all of them to deliver together

.4t(1/4) + .4t(1/t) + .4t(1/(t+1)) = 1
t (0.1 + 0.4/(t + 1)) + 0.4 = 1
t (0.1 + 0.4/(t + 1)) = 0.6
0.1 + 0.4/(t + 1) = 0.6/t
0.4/(t + 1) = (0.6 - 0.1t)/t
0.4t = -0.1t^2 + 0.5t + 0.6
0 = -0.1t^2 + 0.1t + 0.6

use quadratic formula and you'll get t = 3

so Kay can deliver the flyers in 3 hrs alone


2) let x be the speed of Kiran from Tortula to Cactus. Then she increases her speed by 10 mi/hr. That means her speed now is x + 10

distance = speed * time
time = distance/speed

250/x + 360/(x + 10) = 11
360/(x + 10) = (11x - 250)/x
360x = 11x^2 - 140x - 2500
0 = 11x^2 - 500x - 2500

use quadratic formula and you'll get x =50 mi/hr

Answer 3

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