JJJJJJJJJJ
Hey JJJJJJJJJJ,
I'm sure there are a few different approaches to this question but here is my one:
One thing to note about speed-distance-time questions is that if you divide the distance by the speed, you will get time (i.e. hours).
So, to summarise the information in the question:
Walking - 7km at x km/hr
Cycling - 7 km at 4x km/hr
Motoring - 36km at (6x + 3) km/h
TOTAL: 50 km in 4 hours
This means that 7km/x + 7km/4x + 36km/(6x+3) = 4 hours, due to the note I stated above (I left out the km/hr units so that it's not confusing).
So, now you have to do a bit of algebraic gymnastics which I will leave out for the sake of your sanity (however, please do let me know if you would like the working out for this part) and you should get this:
96x2 - 306x - 105 = 0
With some factorisation, you should get 3(16x + 5)(2x - 7) = 0 and due to the null factor law, this means that
x = -5/16 and 7/2
Since x > 0, x = -5/16 is an extraneous solution and therefore, x = 7/2 = 3.5.
You can use this x value to sub back into the original question to check if it's correct.
Hope this helps and let me know if you need more working out or explanation.
