The value of t is:
a) when v = 15 then t = 3 hours
b) when v = 18 then t = 2.52 hours
<h3><u>Solution:</u></h3>
The relation between speed and time taken is given as:

It is given that for first 30 km, the speed of bicyclist is v km/hour
<em><u>
Time taken to cover first 30 km is given by:</u></em>

For next 17 km the speed of bicyclist is 2 km/hour greater than his original speed
so the speed to cover next 17 km = v + 2
<em><u>
Time taken to cover next 17 km is given by:</u></em>

Now total time t spent by the bicyclist to cover entire trip is given by
---- eqn 1
We have to find value of "t" for a) v = 15 and b) v = 18
<u><em>a) value of t when v = 15</em></u>
Substitute v = 15 in eqn 1

t = 2 + 1 = 3
So t = 3 hours
<u><em>b) value of t when v = 18</em></u>

Thus t = 2.52 hours