Time and Distance Formulas relate Time,
Distance and Speed. These relationships have several practical
applications. It is observed that in all the Competitive Exams,
questions based on the concept of Time & Distance are asked.

For
example if you know the speed of any vehicle and the distance covered
by that vehicle, then we can easily calculate the time taken in whole
journey by using the formula of Time and Distance.

Important Formulas

Speed = Distance/Time ,Distance= Speed×Time, Time= Distance/Speed

S km/hr =(s×5/18)m/sec

S m/sec =(s×18/5)km/hr

Example

Taj Express travelling at 5/11 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the Taj Express.

Solution

Suppose the actual speed of Taj = S km/hr

Then new speed = 5/11× S

Time taken by Taj with new speed

= 1 hr 40 min 48 sec

= 1hr+40 × 1/60 hr+48 × 1/(60×60) [Because 1hr = 60 minutes,

1 minute = 60 Second,

& 1 minute = ( 1)/60 hr ,

1 Second = 1/60 minute ]

= 1hr +2/3 hr + 1/75 hr

= 126/75 hrs

Now, according to the formula

New Speed × Time taken by Taj with new speed = Distance covered by Taj

5/11 S× 126/75 = 42

S = (42×75×11)/(126×5)

S =55km/hr

Hence, the actual speed of the Taj Express is 55 km/hr

Points to remember about Time and Distance Segment Problems-

1. Read the units of time speed and distance carefully.

2.
If the distance is given in km and the aped is in m/s then always
convert the units. According to the demand of the question you can
change the kilometer in to meter or m/s in to km /hr.