Thread: Simultaneous equations

Need help on this one please.... Thanks very much.

Sandra can take two alternative routes from Melbourne to Brisbane. If she takes route A she passes through 8 toll booths and takes 19 hours and 10 minutes to get there, and the trip costs her $155.00. If she takes route B she passes through 2 toll booths and takes 21 hours and 40 minutes to get there, costing her $140.00. All toll booths charge the same price. How much does petrol cost Sandra per hour, and what price do the tollbooths cost?

Hi,

We know the toll has to be paid a certain number of times for each trip and is the same, and the running cost will be the same per hour (fuel per hour). The total cost of each trip is known, so if we write the various costs of each trip we get the known total.
Try solving these equations for X and Y. X will be the cost of the toll and Y will be the cost per hour of the trip.


8x + (19+1/6)y = 155

2x + (21+2/3)y = 140

(If you don't get along with fractions very well, you might like to convert the times to minutes, then multiply the final answer by 60)

Have a go at it and let me know if you'd like a worked solution...

[Ans: Toll = $5, Fuel = $6/hr]

Thanks so much for your quick response I will try and figure it out. If I have problems I will get back to you.

Thanks again

Thank you so much spimon I worked it out. It wasn't easy but it was done. (with a lot of help from above) and your self of course.... Thanks a lot and take care.

No worries matey. Definitely better if you do the working yourself so you really understand what's going on. Well done getting the answer!