1. ## Worded linear question

Hi there,

Firstly, I'm not the best with linear worded questions. I am having trouble with one that I would like some help with. However, before anyone helps could someone please let me know the best way or how they go about solving linear worded questions as they can sometimes be confusing.

I know I can come on here to ask for help all the time but I'd like to figure it out on my own eventually.

Thank-you.

An aircraft, used for fire spotting, flies from its base to locate a fire at an unknown distance, x km away. It travels straight to the fire and back, averaging 240km/h for the outward trip and 320km/h for the return trip. If the plane was away for 35 minutes, find the distance, x km.

2. The best way (for me) to go about these questions is to draw a diagram. It may not say much you don't already know but it really helps the visualisation process.

I will go step by step my thought processes when setting up these equations. If you feel you can figure it out from a point, please do continue by yourself and refer back only when you're stuck. Your own thought processes is much better for you than mine.

I draw a simplistic diagram for you here.

BASE ------- x km @ 240 km/h in time t1------> FIRE
BASE <------ x km @ 320 km/h in time t2------ FIRE
Total 35 mins.

Now that you have a diagram look at what you are solving for. You're solving for x, a specific distance.

How can you relate the information you are given with distance?
Let see, we have a time and two speeds. Now we think about what we have learnt and recall that distance = speed x time

There is a trick here. The speed to the fire is different on the return trip, so the time will be different - there will be a time taken $t_1$ to the fire and a different time $t_2$ for the return trip.

Looking at our formula that relates all our information together, we see that time = distance / speed. Luckily we have a total flight time so this becomes a nice little equation:

$t_1 + t_2 = \frac{x}{240 \, kmh^{-1}} + \frac{x}{320 \, kmh^{-1} }= 35 \, mins$

3. ## worded linear problems

Hello Chuck,

An additional important point. Make sure you use consistent units.In this case km/hr must be converted to km/min or mins to hours.

bjh