# Math Help - Quadratic Equations: Word Problems

1. ## Quadratic Equations: Word Problems

"A trip of 720 km is travelled by car. On the return trip, the speed is increased by 10 km/h. The total time spewnt travelling was 17 h. Find the speed each way."
The answer is 80 km/h and 90 km/h, but I have no idea how to get there. In other words, I can't come up with the right equation to start things off.

Sunlis

2. Originally Posted by Sunlis
"A trip of 720 km is travelled by car. On the return trip, the speed is increased by 10 km/h. The total time spewnt travelling was 17 h. Find the speed each way."
The answer is 80 km/h and 90 km/h, but I have no idea how to get there. In other words, I can't come up with the right equation to start things off.

Sunlis
We know that the total travel time is T = 17 h. I am going to set $T = t_1 + t_2$ where the two t's are for the time out and the time back respectively.

Each portion of the trip (out and back) was 720 km.

So
$v_1 = \frac{720 \, km}{t_1}$

$v_2 = \frac{720 \, km}{t_2}$

and we know that $v_2 = v_1 + 10 \, km/h$

Thus
$t_1 = \frac{720 \, km}{v_1}$

$t_2 = \frac{720 \, km}{v_1 + 10 \, km/h}$

Finally we have $t_1 + t_2 = 17 \, h$

Thus
$\frac{720 \, km}{v_1} + \frac{720 \, km}{v_1 + 10 \, km/h} = 17 \, h$

I leave solving this to you. I get $v_1 = 80 \, km/h$ as advertised. (Note: You may discard the negative solution as unphysical.)

-Dan

3. Awesome.
For some reason I just couldn't get myself to think properly for that one.