Question

PLEASE HELP ASAP!!!!

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 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:

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

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 = (v)/(30)`

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

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

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

`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