Problem23:A man travels regularly between two cities. He takes 4(2/3) hours if he travels at his usual speed. He finds that if he increases his speed by 3km/h he can reduce the time taken by 1/3 hour. What is his usual speed?
Problem23: A man travels regularly between two cities. He takes 4(2/3) hours if he travels at his usual speed. He finds that if he increases his speed by 3km/h he can reduce the time taken by 1/3 hour. What is his usual speed?
Solution:
A<———————s—————————–>B
Let the distance between two cities say A & B is ‘s’ kms!!
We use distance formula here;
\[ s=v\times t \]
where,
s= distance
t= time
v= speed
Let usual speed of the man is ‘x’ km/hr
So, in first case,
the distance =s km
speed= ‘x’ km/hr
time = 4(2/3)=14/3 hrs
so, the distance s is;
\[ s=x\times \frac{14}{3}=\frac{14x}{3} \]
Now, in second case;
distance =s km
speed=(x+3)km/hr
time = 14/3-1/3=13/3
So, distance;
\[ s=(x+3)\times \frac{13}{3}=\frac{13(x+3)}{3} \]
Now both cases the distances are same;
so,
\[ \frac{14x}{3}=\frac{13(x+3)}{3} \]
this gives;
\[ 14x=13(x+3) \]
\[ 14x=13x+39 \]
finally,
\[ x=39 km/hr \]
So usual speed is 39 km per hour