SOLUTION: Im having trouble with some word problems i have many for my homework i understand the easy work ones but i thought i put 3 differnt kinds up so that i can finish the rest of my ho
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Question 401310: Im having trouble with some word problems i have many for my homework i understand the easy work ones but i thought i put 3 differnt kinds up so that i can finish the rest of my homework by examples of these ones.Can you please help me?
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 6
___ + ____ =2
x+5 x
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.
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?
For this i have a table and some work done but i think its the 4/3 is throwing me off
time hrs job
amy 4/3x 1 divided by 4/3x
bob x i divided by x
total 1 divided by 12
i divided both sides by 12x(4/3x)
and got 12x+12(4/3x) = x(4/3x)
12x+16x=4/3x^2
28x=4/3x^2
4/3x^2-28x=0
now im stuck
IF someone could please help me that would be wonderfull and i thank you soo much
You can put this solution on YOUR website! 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.
You can put this solution on YOUR website! 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
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