# Time and Distance Part 8

Problem 1: Walking at $\frac{3}{4}$th of his usual speed a man covers a certain distance in 2 hours more than the time taken to cover the distance at his usual speed. The time taken by him to cover the same distance with usual speed is?

Solution:

New     :     Usual

S             3         :          4

t              4         :          3

4-3=1

1——->2

4———>?$(\frac{4\times&space;2}{1})=8$hours

3———->?$(\frac{2\times&space;3}{1})=6$hours

The time is taken by him to cover the same distance with usual speed is 6 hours.

Problem 2: A car traveling with  $\frac{5}{7}$ th of his usual speed covers 42km in 1hr 40 min 40 sec. What is the usual speed of the car?

Solution:

Given time =1hr 40 min 40 sec

$1+\frac{40}{60}+\frac{48}{3600}$

$1+\frac{2}{3}+\frac{1}{75}$

$\frac{75+50+1}{75}=\frac{126}{75}$

$S=7X,S^{1}=5X$

5X——–>42KM

$Speed=\frac{Distance}{Time}$

$5x=\frac{42}{126}\times&space;75$

$x=5$

S=7*5=35

Problem 3: A thief is reported to a policeman. The thief starts running and the policeman chases him when the policeman starts chasing the thief the thief was at the distance of 250km. The thief and the policeman run at the speed of 8km/hr and 9km/hr respectively. Find the time that policeman will take to catch the thief?

Solution:

1 hr———–>1km

1000meters————->60min

2.5*100meters————>6min*2.5

250meters———>15min