Word Problem?

Question

Julie travels 5 hours to and from work everyday. Her average rate of speed to work is 18 miles per hour and her average rate of speed returning is 12 miles per hour. How far is it from her home to work?

Answer 1

18x=12y
x+y=5
x+3/2x=5
x=2 and y=3 distance=36 miles

Answer 2

Given

Time to and from work = 5 hours
average rate of speed to work = 18 hours
Average rate of speed from work = 12 hours
How far from home to work = x

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Formulating the equation

x/18 equals the distance divided by the rate of speed to work.

x/12 equals the distance divided by the rate of speed from work.

the time to and from work equals 5 hours

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The equation becomes

x/18 + x/12 = 5

using 36 as the common denominator

36(x/18) + 36(x/12) = 36(5)

2x + 3x = 180

5x = 180

5x/5 = 180/5

Dividing both sides by 5

x = 36

The answer is 36 miles

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Proof

x/18 + x/12= 5

36/18 + 36/12 = 5

2 + 3 = 5

5 + 5

Answer 3

Although this question can be solved with the speed distance formula; the easiest way is to find the lowest common multiple (LCM) of 12 and 18.
Prime factors of 12 = 1*2*2*3
Prime factors of 18 = 1*2*3*3
LCM = 1*2*2*3*3 = 36

36miles is the distance from home to work.

Answer 4

Time TO work: T [hours]
Time FROM work: (5 - T) [hours]


Distance to work = Distance from work = D [miles]

Average speed TO work = D [miles] / T [hours] = 18 [miles/hour]
Average speed FROM work = D [miles] / (5 - T) [hours]
= 12 [miles/hour]

D/T = 18; D = 18T
D/(5 - T) = 12 -------> 18T / (5 - T) = 12
12(5 - T) = 18T
60 - 12T = 18T
30T = 60

T = 2 hours
(5 - T) = 3 hours

Since D/T = 18 [miles/hour] ----> D = 2 [hours] * 18 [miles/hour]
D = 36 miles

Answer 5

(rate) × (time) = (Distance)

Let t be the amount of time Julie drives from home to work.
Going to work: (18mph) × (t hours) = 18t miles

Julie's total time is 5 hours, so however long it takes to get to work, the trip home will be that time subtracted from 5 hours.

Going home: (12mph) × [(5 - t) hours] = 12(5 - t) miles

The distance to work is the same as from work, so set the distances equal and solve.

18t = 12(5 - t). [Distribute.]
18t = 60 - 12t. [Add 12t to both sides.]
30t = 60. [Divide by 30.]
t = 60 / 30 = 2.

t, defined (above) to be the time from home to work, is 2 hours. The question asks how FAR is it... meaning the distance.

18t = 18(2) = 36 miles. It's 36 miles to her workplace.

Answer 6

this question makes no since because if you travel at 18 mph for 5 hours you have traveled 90miles to work and to travel 12mph for 5hrs home you have only gone 60miles and are still 30 miles from home. Clearly this person hit some nasty traffic and took longer than 5hrs to get home. I think she needs to find a job closer to home too. With gas prices as high as they are the commute cant be worth the drive.

Answer 7

Let the distance to the work = x
Since the average speed to work = 18m/hour
Therefore time taken to work = Distance/ average speed
= x / 18......................(i)
The average speed from work = 12 m/hour
and the time taken from work = x/12......................(ii)
Therefore total time to work and from work = x/18 + x/12........(iii)
But the total time given is = 5 hours..................(iv)
From (iii) and (iv) we get
x/18 + x/12 = 5
x( 1/18 + 1/12) =5
x (12 +18)/18. 12 =5
x(30)/18.12 =5
Therefore x = 5.12.18/30
x =36 miles

Answer 8

suppose x as the time she goes to work
suppose y as the time she returning
so 18x=12y
x+y=5
u can get x=2,y=3
3*12=36
or 2*18=36
so the distance is 36

Answer 9

d is distance.

d miles/18 mph + d miles/12 mph = 5 hours

Multiply through by 36:

2d + 3d = 180
5d = 180
d = 36 miles

Answer 10

formula: RT=D Rate times time =Distance

12(5-T)=18T

60-12T = 18T
+12T +12T

60 = 30T

60/30 = 30T/30

2 = T

Answer:

To work: 18(2)=36 miles
From Work : 12(3)= 36miles

Julie lived 36miles from work.