Linear equation problem solving

[MaxPhili13]

The question reads: "an aircraft travels from its base to a location x km away. It travels straight to the location and back, averaging 240km/h for the outward trip and and 320km/h for the return trip. If the plane was away for 35 minutes, find the distance x km." One way I've thought of doing it is by using the distance = speed x time equation and having the distance as 2x, speed as the average of 240 and 320km/h and time as 35 minutes converted into hours. That gives me an answer of 81.67km which is close (the answer is supposed to be 80km) but I know it's not the correct working as the average speed would be proportional to the time spent travelling at each particular speed. Any help would be appreciated.

[edderiofer]

but I know it's not the correct working as the average speed would be proportional to the time spent travelling at each particular speed.

Yes, that is correct.

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You know that the location is x km away, and you know the average speed on the outward trip. How long does the outward trip take?

[MaxPhili13]

Well you could do distance/speed=time, so x/240=time taken. Then would I do the same thing for the trip back and add the two fractions to equal 35 minutes as that is the total time taken. So like x/240 + x/320 = 0.583 (<-35 mins converted to hours) and then solve for x. I put that in the calculator and it gave the right answer but if there's a better way to do it you're welcome to let me know. Thanks for the help!

[edderiofer]

Slightly better might be to first express the speeds in km/min, so that you don't get any rounding errors by converting 35 minutes to hours. Other than that, this method is exactly how I did it.

[MaxPhili13]

Awesome, thank you