Question

a man could be 5 minutes late to reach its destination if he rides his bike at 30 km per hour but he would be 10 minutes early if he died at the speed of 40 km per hour what is the distance of his destination from the he starts?

Answer 1

5 minute late distance 30 km
10 minutes early speed 40 km
10-5=5
40 km -30 km
10 km

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The required distance is 1800 km.}}}$

Step-by-step explanation:

Let 'd' km represents the distance between the destination and the starting points and 't' hours be the time required to reach the destination.

According to the given information, we have

$\dfrac{d}{t+5}=30\\\\\Rightarrow d=30t+150~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$\dfrac{d}{t-10}=40\\\\\Rightarrow d=40t-400~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Comparing equations (i) and (ii), we get

$30t+150=40t-400\\\\\Rightarrow 40t-30t=150+400\\\\\Rightarrow 10t=550\\\\\Rightarrow t=\dfrac{550}{10}\\\\\Rightarrow t=55.$

Substituting the value of 't' in equation (i), we get

$d=30\times55+150=1650+150=1800.$

Thus, the required distance is 1800 km.