1. ## Help on some distance problems please?

Hello...I'm pretty new to this forums (this is my first post) and I think it would be pretty helpful to me. I'm in Grade 9 and I'm looking for some help on distance problems.

I just need an explanation of understanding the question and writing the equation for the problems...solving it is the easy part but the real problem is figuring out the equation. If anybody can help, it would be great (helping me with one would be great already...there's actually 10 questions but I just didn't get 4 of them).

1. Mr. Hill drives to work in Toronto. One day his average speed going to work was 80 km/h but returning it was only 70hm/h. If his total travelling time that day was 3 hours, how far from Toronto is his home?

2. Two guides hiked out on a trail and back again in 45 minutes. Their velocity on the way out was 4km/h and on the way back it was only 3km/h. How far out did they go?

3. The Himalayan Hikers left on a hike at 12 noon on the first day of DST and walked at 4km/h. Stanley forgot to set his clock ahead and arrived one hour late for the start. However, he started out and overtook the others at 4PM. What was Stanley's rate of speed?

4. A freight train travelling at 96hm/h takes two hours longer to cover a certain distance than a passenger train travelling at 120hm/h. Find the distance.

Thanks a bunch. Please...I am asking you DO NOT post the solution. Just need to know how to form and equation...

2. Originally Posted by nathan02079
Hello...I'm pretty new to this forums (this is my first post) and I think it would be pretty helpful to me. I'm in Grade 9 and I'm looking for some help on distance problems.

I just need an explanation of understanding the question and writing the equation for the problems...solving it is the easy part but the real problem is figuring out the equation. If anybody can help, it would be great (helping me with one would be great already...there's actually 10 questions but I just didn't get 4 of them).

1. Mr. Hill drives to work in Toronto. One day his average speed going to work was 80 km/h but returning it was only 70hm/h. If his total travelling time that day was 3 hours, how far from Toronto is his home?
we use the formula $\mbox{Speed } = \frac {\mbox {Distance}}{\mbox{Time}}$

Let $t_1$ be the time he takes to drive to Toronto
Let $t_2$ be the time he takes to drive back
Then $T = t_1 + t_2$ is the total time for the trip (we are told T = 3)
Let $d$ be the distance

Now, since $\mbox{Time } = \frac {\mbox { Distance}}{\mbox{Speed}}$

we have that $t_1 = \frac {d}{80}$ and $t_2 = \frac d{70}$

thus, $T = t_1 + t_2 = \frac d{80} + \frac d{70} = 3$

Now solve for $d$

the other problems are very similar, try them and see what you get

3. Hello, Nathan!

Welcome aboard!

Jhevon's explanation is excellent.

We will use: . $\text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}$

4. A freight train travelling at 96 km/h takes two hours longer to cover
a certain distance than a passenger train travelling at 120 km/h.
Find the distance.
Let $d$ = the distance.

The freight train travels $d$ km at 96 km/hr.
. . This takes $\frac{d}{96}$ hours.

The passengener train travels $d$ km at 120 km/hr.
. . This takes $\frac{d}{120}$ hours.

We are told that the freight's time is two hours more than the passenger's.

There is our equation: . $\frac{d}{96} \;=\;\frac{d}{120} + 2$

3. The Himalayan Hikers left on a hike at 12 noon at 4 km/hr.
Stanley started one hour later and overtook the others at 4PM.
What was Stanley's rate of speed?
We will use a variation of the formula: . $\text{Speed} \:=\:\frac{\text{Distance}}{\text{Time}}$

Here's a back-door approach to this problem . . .

The Hikers walked from noon to 4:00 (four hours).
. . At 4 km/hr, they walked: . $16$ km.

Stanley covered the same distance in 3 hours.

Therefore, his speed was: . $\frac{16}{3} \:=\:5\frac{1}{3}$ km/hr

4. Thanks a lot =)
Helped me a bunch!