This article will equip you to solve all time, speed and distance word problems.

Time & Distance 

Distance = Speed × Time. 

Using this formula, all basic problems can be handled. However, you need to make sure about the correct usage of units while using the above formulas.

Speed is inversely proportional to the time taken when distance travelled is constant. So when speed increases, time decreases and vice versa.

Average Speed

Average Speed = Total Distance covered / Total Time Taken

When the distance is constant: 

            Average speed = 2xy/x+y; 

           Where, x and y are the two speeds at which the same distance has been covered.

When time taken is constant: 

             Average speed = (x + y)/2; 

              Where, x and y are the two speeds at which we traveled for the same time

Relative Speed

If two trains moving in same direction with a speed of S1 & S2 respectively.

            Then the Relative speed will be = S1 –S2

If two trains moving in Opposite Direction 

           Then the Relative speed will be = S1  + S2

Conversion of km / hr into m / s vice versa:

               Km/hr --- 1 km =1000m & 1hr=3600sec

               1000/3600 = 5/18 

  a) km/hr can be converted into m/s multiplying by 5/18.

   b) m/s can be converted to km/hr multiplying by 18/5.

Distance

If a train of length L1 crosses another train of length L2/ a bridge of length l2/a platform of length l2 then the total distance = L1 + L2.

If a train of length L crosses a person or a lamp post then total distance L (because the length of the person or lamp post will be treated as 0 w.r.to train length)

A train of length 800 m crosses a pole in 24 seconds. Find the speed of the train in km/hr.

a) 130 km/hr                 b) 140 km/hr                 c) 100 km/hr                 d) 120 km/hr

Solution:

S = D / T = 800 / 24 m/sec

S = (800 / 24) × (18 / 5) km/hr = 120 km/hr

Note: If a train crosses a pole, then Distance = Length of the train

Answer: d

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