For the first 30 km, the bicyclist rode with a speed of v km/hour. For the remaining 17 km he rode with a speed which was 2 km/hour greater than his original speed. How much time did the bicyclist spend on the entire trip? Let t be the time (in hours), and find t if:

The time spent by bicyclist on entire trip is [tex]t=\frac{30}{v} +\frac{17}{v+2}[/tex]a) when v = 15 then t = 3 hoursb) when v = 18 then t = 2.52 hoursSolution:The time taken is given by formula:[tex]\text {time taken}=\frac{\text {distance}}{\text {speed}}[/tex]For the first 30 km, the bicyclist rode with a speed of v km/hourHere distance = 30 km and speed = v km\hourLet [tex]t_1[/tex] denote time taken to cover first 30 km[tex]t_1 = \frac{v}{30}[/tex]For the remaining 17 km he rode with a speed which was 2 km/hour greater than his original speedso the speed to cover next 17 km = v + 2Let [tex]t_2[/tex] denote time taken to cover remaining 17 km[tex]t_{2} =\frac{17}{v+2}[/tex]Now total time t spent by the bicyclist to cover entire trip is given bytotal time "t" = time taken for first 30 km + time taken for remaining 17 km[tex]t=t_{1} +t_{2}\\\\t=\frac{30}{v} +\frac{17}{v+2}[/tex]We have to find value of "t" for a) v = 15 and b) v = 18a) value of t when v = 15Substitute 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 = 3So t = 3 hoursb) 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