Question

The time taken to complete a journey varies directly as the distance (d) and inversely as the average speed (s).

Answer 1

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,

$3=k \frac{280}{80} [/tex3 = k* 3.5[tex] \frac{3}{3.5} =\frac{k*3.5}{3.5}$ 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!