# Thread: Simultaneous and linear equations

1. ## Simultaneous and linear equations

A rower travels upstream at 6 km per hour and back to the starting place at 10 km per hour. The total journey takes 48 minutes. How far upstream did the rower go?

A man travels from A to B at 4km/h and then from B and A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled.

2. Originally Posted by delicate_tears
A rower travels upstream at 6 km per hour and back to the starting place at 10 km per hour. The total journey takes 48 minutes. How far upstream did the rower go?
...
If
v is the speed
d is the distance
t is the time
then you are supposed to know that $v=\frac dt$

Let x be the distance and y be the time rowing upstream then you have
total time t = 0.8 h = 48 min
rowing upstream: y
rowing downstream 0.8 h - y

$\left| \begin{array}{r}6=\frac xy\\10 = \frac x{0.8-y}\end{array}\right.$ .... Multiply by the denominators: $\left| \begin{array}{r}6y= x\\10(0.8-y) = x \end {array} \right.$

Substitute x by 6y:

$8-10y = 6y~\iff~y=\frac12$

The rower needs half an hour to row upstream by a speed of 6 $\frac{km}{h}$ that means the distance upstream is 3 km.

3. Originally Posted by delicate_tears
...

A man travels from A to B at 4km/h and then from B and A at 6 km/h. The total journey takes 45 minutes. Find the distance travelled.
Let d be the distance between A and B.

From $v=\frac dt$ you get: $t=\frac dv$. With your problem:

$\frac d4 + \frac d6 = \frac34$ .......... Multiply by 24:

$6d + 4d = 18~\iff~d=1.8$

The total distance is therefore 3.6 km