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.
i made a table
D R T 
run 8mi x+5 
walk 6mi x 
total 2hrs 
i came up the equation 
8/(x+5) + 6/x = 2 
Multiply thru by x(x+5) to get:
8x + 6(x+5) = 2x(x+5)
14x+30 = 2x^2+10x
---
2x^2-4x-30 = 0
---
x^2-2x-15 = 0
(x-5)(x+3) = 0
Positive solution:
x = 5 mph (walking rate)
---
x+5 = 10 mph (jogging rate)
===============================


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? 
Im not sure how to get this one except i know to divide distance by time and the distance is 100 and the time is x-1 and the rate is x+5 i think i dont know how to set this up.
---
Original DATA:
dist = 100 ; rate = x mph ; time = d/r = 100/x hrs
------
New DATA:
dist = 100 ; rate = x+5 mph ; time = 100/(x+5) hrs
---
Equations:
old time - new time = 1 hr
100/x - 100/(x+5) = 1
Multiply thru by x(x+5) to get:
100x+500 - 100x = x(x+5)
x^2+5x-500 = 0
(x-20)(x+25) = 0
Positive solution:
x = 20 mph
x+5 = 25 mph
======================  

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? 
----
Together time = 12 hr/job ; rate = 1/12 job/hr
Let Bob time = x hr/job ; Bob's rate = 1/x job/hr
Amy's time = (4x/3) hr/job ; Amy's rate = 3/(4x) job/hr
-----
Equation:
rate + rate = together rate
1/x + 3/(4x) = 1/12
Multiply thru by 12x to get:
12 + 9 = x
x = 13 hrs (Bob's time)
(4/3)x = (4/3)13 = 52/3 = 17 1/3 hrs (Amy's time)
===================
Cheers,
Stan H.