Question

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: v=18

Answer 1

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

$t_{1} =\frac{30}{v}$           ( $time=\frac{distance}{speed}$)

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

$t_{2} =\frac{17}{v+2}$

now total time t spent by the bicyclist to cover entire trip is given by

$t=t_{1} +t_{2}$

$t=\frac{30}{v} +\frac{17}{v+2}$

now if v=18 , we have

$t=\frac{30}{18} +\frac{17}{20}$

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

$t=\frac{30(10)}{18(10)} +\frac{17(9)}{20(9)}$$t=\frac{300}{180} +\frac{153}{180} =\frac{300+153}{180}$

$t=\frac{453}{180} =2.52$ hours (approx)