Respuesta :
Answer:
t= 2.52 hours
Step-by-step explanation:
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{30}{v}[/tex] ( [tex]time=\frac{distance}{speed}[/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}[/tex]
[tex]t=\frac{30}{v} +\frac{17}{v+2}[/tex]
now if v=18 , we have
[tex]t=\frac{30}{18} +\frac{17}{20}[/tex]
now to add fractions we make the denominator same
Hence we will find the LCM of 18 and 20
LCM of 18 and 20 = 180
now we need to make both the denominator equal to 180
[tex]t=\frac{30(10)}{18(10)} +\frac{17(9)}{20(9)}[/tex][tex]t=\frac{300}{180} +\frac{153}{180} =\frac{300+153}{180}[/tex]
[tex]t=\frac{453}{180} =2.52[/tex] hours (approx)
