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:

a) v=15
b) v=18

Answer 1

The time spent by bicyclist on entire trip is
`t=(30)/(v) +(17)/(v+2)`

a) when v = 15 then t = 3 hours

b) when v = 18 then t = 2.52 hours

Solution:

The time taken is given by formula:

`\text {time taken}=\frac{\text {distance}}{\text {speed}}`

For the first 30 km, the bicyclist rode with a speed of v km/hour

Here distance = 30 km and speed = v km\hour

Let
`t_1` denote time taken to cover first 30 km

`t_1 = (v)/(30)`

For the remaining 17 km he rode with a speed which was 2 km/hour greater than his original speed

so the speed to cover next 17 km = v + 2

Let
`t_2` denote time taken to cover remaining 17 km

`t_(2) =(17)/(v+2)`

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

total time "t" = time taken for first 30 km + time taken for remaining 17 km

`t=t_(1) +t_(2)\\\\t=(30)/(v) +(17)/(v+2)`

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

`t=(30)/(v)+(17)/(v+2)=(30)/(15)+(17)/(15+2)`

t = 2 + 1 = 3

So t = 3 hours

b) value of t when v = 18

`\begin{array}{l}{t=(30)/(v)+(17)/(v+2)=(30)/(18)+(17)/(18+2)=1.67+0.85} \\\\ {t=2.52}\end{array}`

Thus t = 2.52 hours