d 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? | Job Exam Rare Mathematics (JEMrare) - Solved MCQs
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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

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