question_answer

The time taken by a person to cover 150 km was \[2\frac{1}{2}\] hours more than the time taken is return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in each direction.

Answer:

Let the speed while going be \[x\text{ }km/h\]

Time taken by a person to cover \[150\text{ }km=\frac{150}{x}hours\]

Time taken by a person in return journey \[=\frac{150}{x+10}\] hours

Now, according to the given condition, \[=\frac{150}{x}-\frac{150}{x+10}=\frac{5}{2}\]

\[\frac{150(x+10-x)}{x(x+10)}=\frac{5}{2}\]

\[300\times 10=5x(x+10)\]

\[3000=5{{x}^{2}}+50x\]

\[5{{x}^{2}}+50x-3000=0\]

\[{{x}^{2}}+10x-600=0\]

\[{{x}^{2}}+30x-20x-600=0\]

\[x(x+30)-20(x+30)=0\]

\[(x-20)(x+30)=0\]

\[x=20\] or \[x=-30\] (neglect)

Hence, the speed while going is \[20\text{ }km/h\] and the speed while returning is \[30\text{ }km/h\]