Problem Solving w/ Equations ('distance', fractions)

I am currently taking summber school; it's pretty intense, and I currently have the lowest mark in class

We have come across a subject with which I'm having trouble. I just can't seem to find the equations for word problems. Could someone give me some tips on doing them?

Here are two of the questions in my homework:

1) Venus orbits the sun in 4 days less than one third of the time Mars takes to orbit the sun. Venus orbits the sun in 225 days. How many days does Mars take to orbit the sun?

2) Indira and Ben drove from Winnipeg to Dauphin Lake and back. Indira drove from Winnipeg to Dauphin Lake at 100km/h. Ben drove on the return trip at 80km/h. Their total driving time was 6.75 h. What is the distance, in kilometres, from Winnipeg to Dauphin Lake?

If someone could take me step by step and show me how its done that would be great. Thank you!

Re: Problem Solving w/ Equations

Hello what1sth1s!

1) Venus orbits the sun in 4 days less than one third of the time Mars takes to orbit the sun. Venus orbits the sun in 225 days. how many days does Mars take to orbit the sun?

Click to expand...

We will let Venus' time be: \(\displaystyle \L \; v\)

We will let Mars' time be: \(\displaystyle \;\L m\)

So: \(\displaystyle \;\frac{1}{3}m-4=v\)

Since: \(\displaystyle \;v=225\)

Hence: \(\displaystyle \;\frac{1}{3}m-4\;=\;225\)

Addition Property \(\displaystyle (+4)\): \(\displaystyle \;\frac{1}{3}m=229\)

Division Property \(\displaystyle (\frac{1}{3})\): \(\displaystyle m=687\)

So it takes Mars 687 days to orbit the sun.

2) Indira and Ben drove from Winnipeg to Dauphin Lake and back. Indira drove from Winnipeg to Dauphin Lake at 100km/h. Ben drove on the return trip at 80km/h. Their total driving time was 6.75 h. What is the distance, in kilometres, from Winnipeg to Dauphin Lake?

Click to expand...

We will let Indira's time be: \(\displaystyle \L \; i\)

We will let Ben's time be: \(\displaystyle \L \;b\)

So: \(\displaystyle \; i+b=6.75\;\Rightarrow\;i=6.75-b\)

Also we can derive: \(\displaystyle \: d=100i\; & \;d=80b\)

Now we need to use subsitution: \(\displaystyle 100(6.75-b)=80b\)

When you get \(\displaystyle b\) fill it back in \(\displaystyle d=80b\) and you will get the distance from Winnipeg to Dauphin Lake. Back solve for \(\displaystyle i\) and plug it into \(\displaystyle d=100i\) and you should get the same distance.

Hope this helps.

Re: Problem Solving w/ Equations

Since you posted these exercises to the "arithmetic" category, rather than to either of the "algebra" categories, I will guess that you haven't yet taken algebra and aren't very (or at all) familiar with variables.

what1sth1s said:

1) Venus orbits the sun in 4 days less than one third of the time Mars takes to orbit the sun. Venus orbits the sun in 225 days. how many days does Mars take to orbit the sun?

Click to expand...

If Venus is four less than one-third, then add four to get one third. Then multiply by three to get the whole.

what1sth1s said:

2) Indira and Ben drove from Winnipeg to Dauphin Lake and back. Indira drove from Winnipeg to Dauphin Lake at 100km/h. Ben drove on the return trip at 80km/h. Their total driving time was 6.75 h. What is the distance, in kilometres, from Winnipeg to Dauphin Lake?

Click to expand...

Going one way, they covered 100 km in an hour. Going back the other way, they covered 80 km in one hour. That is, for every 5 km one way in three minutes, they moved 4 km going the other way. To have covered the same distance, they need then to have travelled for 5/4 as long when they came back as when they went out. That is, they "went" for 4/4 of the "going" time, and they "came" for 5/4 of the "going" time.

So divide the 6.75 hours into nine parts. Assign four of the parts to the "going" portion and five of the parts to the "coming" portion. Multiply by the rates, and verify that the distances are the same.

Eliz.