Question

PLEASE HELP ASAP!!!!

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:

$t_1 = \frac{v}{30}$

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:

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

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

$t=t_{1} +t_{2}\\\\t=\frac{30}{v} +\frac{17}{v+2}$  ---- 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

$t=\frac{30}{v}+\frac{17}{v+2}=\frac{30}{15}+\frac{17}{15+2}$

t = 2 + 1 = 3

So t = 3 hours

b) value of t when v = 18

$\begin{array}{l}{t=\frac{30}{v}+\frac{17}{v+2}=\frac{30}{18}+\frac{17}{18+2}=1.67+0.85} \\\\ {t=2.52}\end{array}$

Thus t = 2.52 hours