# Linear equations question grade 10

• Jun 4th 2013, 09:15 AM
xXplosionZz
Linear equations question grade 10
Need help with this one, would be appreciated if you could tell me how to solve this question.

Dahlia walks from her house to school at 2km/h. After school she jogs back home at 6km/h and saves 15mins. how far does Dahlia live from school?

Thanks!(Hi)
• Jun 4th 2013, 12:30 PM
MINOANMAN
Re: Linear equations question grade 10
solve the equation 2x = 6(x-1/4) for x and find the time in hours .
then multiply 2x to find the distance in KM ... as simple as such
• Jun 4th 2013, 12:43 PM
HallsofIvy
Re: Linear equations question grade 10
Quote:

Originally Posted by xXplosionZz
Need help with this one, would be appreciated if you could tell me how to solve this question.

Let t be the time it takes Dahlia to walk to school at 2 km/h in hours, x the distance she lives from school in km.

Quote:

Dahlia walks from her house to school at 2km/h.
speed= distance divided by time so $\displaystyle \frac{x}{t}= 2$. that is equivalent to x= 2t.

Quote:

After school she jogs back home at 6km/h and saves 15mins. how far does Dahlia live from school?
So $\displaystyle \frac{x}{t- 1/4}= 6$. That is equivalent to x= 6(t- 1/4). Together with x= 2t, x= 2t= 6t(t- 1/4). Solve that for t then use x= 2t to find x.

Quote:

Thanks!(Hi)
• Jun 4th 2013, 02:19 PM
Soroban
Re: Linear equations question grade 10
Hello, xXplosionZz!

Quote:

Dahlia walks from her house to school at 2km/h.
After school she jogs back home at 6km/h and saves 15mins.
How far does Dahlia live from school?

Recall the formula: .$\displaystyle \text{Distance} \:=\:\text{Speed} \times \text{Time}$
. . We have: .$\displaystyle D \:=\:S\cdot T \quad\Rightarrow\quad T \:=\:\frac{D}{S}$

Let $\displaystyle x$ = distance to school (in kilometers).

She walks $\displaystyle x$ km at 2 km/h.. This takes: $\displaystyle \tfrac{x}{2}$ hours.

She jogs $\displaystyle x$ km at 6 km/h.. This takes: $\displaystyle \tfrac{x}{6}$ hours.

Her jogging time is a $\displaystyle \tfrac{1}{4}$-hour less than her walking time.

Our equation is: .$\displaystyle \frac{x}{6} \;=\;\frac{x}{2} - \frac{1}{4}$

Go for it!
• Jun 4th 2013, 05:09 PM
xXplosionZz
Re: Linear equations question grade 10
Thanks everyone, I got it!
• Jun 5th 2013, 06:41 AM
bjhopper
Re: Linear equations question grade 10
another way

km/hr x hr = km
2t1 =d=6t2
t1=3t2
t1-t2=1/4
3t2-t2=1/4
t2 = 1/8 hr
d=6/8 =3/4 km