1. ## distance over time

a student walks y kilometres at 3km/h

i) write down an expression for the time, in hours that he takes.

ii) he then walks a further y+3 kilometres at 4km/h. the total walking time is 4 hours and 50 minutes. write down the equation in y and solve it.

2. Originally Posted by simonmann
a student walks y kilometres at 3km/h

i) write down an expression for the time, in hours that he takes.

ii) he then walks a further y+3 kilometres at 4km/h. the total walking time is 4 hours and 50 minutes. write down the equation in y and solve it.
$\displaystyle speed=\frac{distance}{time}$

Solve for time: $\displaystyle \frac{y}{t}=3~\implies~t=\frac y3$

The next part of his walk:

$\displaystyle \frac{y+3}t=4~\implies~ t=\frac{y+3}4$

Both periods together are $\displaystyle \frac{29}6\ h$

$\displaystyle \frac y3 + \frac{y+3}4 = \frac{29}6$

Solve for y. I've got: $\displaystyle \boxed{y = 7\ km}$

3. distance = rate*time

$\displaystyle d=rt$

$\displaystyle t=\frac{d}{r}$

$\displaystyle t_1=\frac{y}{3}$
$\displaystyle t_2=\frac{y+3}{4}$

$\displaystyle t_1+t_2=\frac{y}{3}+\frac{y+3}{4}=\frac{29}{6}$

$\displaystyle 4y+3y+9=58$

$\displaystyle 7y=49$

$\displaystyle y=7km$

Too fast for me Earboth!!