Given that, the time (t) taken to complete a journey varies directly as the distance (d) and inversely as the average speed (s).
Hence, we can set an equation as following:
t = k\frac{d}{s}
Other information is that it takes 3 hours to complete a 280km trip at 80km/h.
So, plug in t = 3, d = 280 and s = 80 in the above equation to get the value of k. Therefore,
[tex] 3=k \frac{280}{80} [/tex
3 = k* 3.5
[tex] \frac{3}{3.5} =\frac{k*3.5}{3.5} [/tex] Divide each sides by 3.5.
k = 0.857142857
So, k = 0.857
Now we need to find the time when d= 546 and s = 65. So, plug in these values in the above equation to get the value of t. Hence,
t = 0.857*\frac{546}{65}
= 0.857 * 8.4
= 7.1988
= 7 hours ( Rounded to nearest integer).
So, it will take 7 hours.
Hope this helps you!
