Question 401310
1)A jogger ran 8 miles and then walked 6miles. The jogger's running speed was 5 miles per hour faster then her walking speed. Th total time for jogging and walking was 2 hrs find the joggers walking speed and jogging speed.

let x=walking speed
then x+5=running speed
travel time = distance/speed

(6/x)+(8/(x+5))=2
LCD=x(x+5)
6(x+5)+8x=2x(x+5)
6x+30+8x=2x^2+10x
2x^2-4x-30=0
x^2-2x-15=0
(x-5)(x+3)=0
x-5=0
x=5
x+3=0
x=-3 (reject)
ans:
walking speed=5 miles per hour
jogging speed = x+5 = 10 miles per hour 


2)Another one i cant figure out is A car travels for 100miles at a uniform speed. If the speed is increased by 5 miles per hour, the trip would take one hour less time. What is the car's original speed?

let x=car's original speed
then x+5= car's faster speed
travel time = distance/speed

100/x-100/(x+5)=1
100(x+5)-100x=x(x+5)
100x+500-100x=x^2+5x
x^2+5x-500=0
(x+25)(x-20)=0
x+25=0
x=-25 (reject)
x-20=0
x=20
ans: The car's original speed=20 miles per hour

3) Working together amy and bob can complete a job in 12 hours. Working alone it takes amy 4/3 as much time as bob to do the job how long will it take each to do the job working alone?

let x=hours Bob can do the job alone
his hourly rate would then be 1/x
let(4/3)x=4x/3 hours Amy can do the job alone
her hourly rate would then be 3/4x (1/(4x/3)=3/4x)
working together they can complete the job in 12 hours
so, their hourly rate working together=1/12
sum of hourly rates of individuals = hourly rate working together

(1/x)+(3/4x)=1/12
LCD=4x
4+3=x/3
7=x/3
x=21
ans: 
Bob can do the job alone in 21 hours
Amy can do the job alone in 4/3*21=28 hours