Answer :
The value of t is:
a) when v = 15 then t = 3 hours
b) when v = 18 then t = 2.52 hours
Solution:
The relation between speed and time taken is given as:
[tex]\text {time taken}=\frac{\text {distance}}{\text {speed}}[/tex]
It is given that for first 30 km, the speed of bicyclist is v km/hour
Time taken to cover first 30 km is given by:
[tex]t_1 = \frac{v}{30}[/tex]
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
Time taken to cover next 17 km is given by:
[tex]t_{2} =\frac{17}{v+2}[/tex]
Now total time t spent by the bicyclist to cover entire trip is given by
[tex]t=t_{1} +t_{2}\\\\t=\frac{30}{v} +\frac{17}{v+2}[/tex] ---- eqn 1
We have to find value of "t" for a) v = 15 and b) v = 18
a) value of t when v = 15
Substitute v = 15 in eqn 1
[tex]t=\frac{30}{v}+\frac{17}{v+2}=\frac{30}{15}+\frac{17}{15+2}[/tex]
t = 2 + 1 = 3
So t = 3 hours
b) value of t when v = 18
[tex]\begin{array}{l}{t=\frac{30}{v}+\frac{17}{v+2}=\frac{30}{18}+\frac{17}{18+2}=1.67+0.85} \\\\ {t=2.52}\end{array}[/tex]
Thus t = 2.52 hours