# Math Help - Linear equations question grade 10

1. ## 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!

2. ## 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

3. ## Re: Linear equations question grade 10

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.

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.

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.

Thanks!

4. ## Re: Linear equations question grade 10

Hello, xXplosionZz!

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!

5. ## Re: Linear equations question grade 10

Thanks everyone, I got it!

6. ## 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