• Dec 3rd 2006, 11:19 AM
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
• Dec 3rd 2006, 11:28 AM
topsquark
Quote:

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
• Dec 3rd 2006, 11:44 AM
Sunlis
Awesome.
For some reason I just couldn't get myself to think properly for that one.