# Linear equations question grade 10

• Jun 4th 2013, 09:15 AM
xXplosionZz
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 $\frac{x}{t}= 2$. 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 $\frac{x}{t- 1/4}= 6$. 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: . $\text{Distance} \:=\:\text{Speed} \times \text{Time}$
. . We have: . $D \:=\:S\cdot T \quad\Rightarrow\quad T \:=\:\frac{D}{S}$

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

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

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

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

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

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