Desperately need help with word problems

[StrugglesWithMath]

Don't need help any longer, thanks.

Content removed by author -- going with answers I was checking because they were my answers and I am going to remain confident I got them right and any other questions have been answered. Thanks! Whole thread can be removed to help with server space (if it matters) unless site wants to keep it up.

 

[soroban]

Hello, StrugglesWithMath!

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 \(\displaystyle a\) = number of hours for Amy to do the job alone.
In one hour, she can do \(\displaystyle \frac{1}{a}\) of the job.
. . In 12 hours, she can do \(\displaystyle \frac{12}{a}\) of the job.

Let \(\displaystyle b\) = number of hours for Bob to do the job alone.
In one hour, he can do \(\displaystyle \frac{1}{b}\) of the job.
. . In 12 hours, he can do \(\displaystyle \frac{12}{b}\) if the job.
But in 12 hours, they will complete the job: .\(\displaystyle \dfrac{12}{a} + \dfrac{12}{b} \:=\:1\) .[1]

We are told that: .\(\displaystyle a = \frac{4}{3}b\)

Substitute into [1]: .\(\displaystyle \dfrac{12}{\frac{4}{3}b} + \frac{12}{b} \:=\:1\)

Multiply by \(\displaystyle \frac{4}{3}b:\;\;12 + 16 \:=\:\frac{4}{3}b\)

Therefore: .\(\displaystyle \begin{Bmatrix}b \,=\, 21 \\ a \,=\, 28 \end{Bmatrix}\)

 

[Deleted member 4993]

Okay, story problems are my weakness. I need help. Two of the four problems I have attempted to answer, so maybe if someone can double check my answers. I need help pulling the info out and figuring out the equations that need to be solved. They need to be solved using complex fractions if applicable or rational equations. for me, solving is not the problem I have, it is setting up the problem.

1) A jogger ran 8 miles and then walked 6 miles. The jogger's running speed was 5mph faster than her walking speed. the total time for jogging and walking was 2 hours. Find the jogger's walking speed and jogging speed is extra. I came up with walking speed of 5mph and a jogging speed of 10mph. I did this by solving with the following fractions: (x being the walking speed)

6/x + 8/(x+5) = 2/1 x=5 so running would be x+5

2)A car travels for 100 miles at a uniform speed. If the speed is increased by 5mph, the trip would take one hour less time. What is the car's original speed?
*I had no idea how to set this one up.

Let the original speed = S and original time = t

distance traveled is constant = 100 miles

so

100 = S * t .............................................................(1)

and

100 = (S+5)(t-1) → 100 = S*t - S +5*t - 5 → 100 + 5 - 100 = 5*t - S → 5 = 5*100/S - S

You can solve for 'S' from above.

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?
*again, confused on set up
4)Mary and her mother Gladys have decided to wallpaper a room together. Working alone, mary would need 18 hours, but gladys only requires 12 to complete the same job. How long will it take them to get it done, working together?

On this one I set up as follows:
1/18 + 1/12 = 1/x

The answer I found is that it would take 7 1/5 or 7hrs 12min for them to do it together.

Please help! do I have the ones I did right? and how do I set the others up?!?!

.