Question

A takes 3 hours more than B to walk 30 km. But, if A doubles his pace, he is ahead of B by hours. Find their speed of walking
 A. A’s speed=5 km/hr, B’s speed=8km/hr
B. A’s speed=15/2 km/hr, B’s speed=6 km/hr
C. A’s speed=10/3 km/hr, B’s speed=5 km/hr
D. Data insufficient

Answer 1

Hint: In this question the first thing that you should do is to write down the formula for finding speed. Its formula is $ Time = \dfrac{{Dis\tan ce}}{{Speed}} $ , where time = time taken by object, distance = distance travels by object and speed = in which speed object moves. Finally put the value in the formula to get the answer.

Complete step-by-step answer:
In this question, it is given that :
Time taken by A is 3 hour more than B and if speed of A is double than he is ahead of B by $ \dfrac{3}{2} $ hours
Total distance = 30 km.
Let the speed of A be x km/hr and the speed of B is y km/hr.
We know that relation between distance travelled , speed and time taken is given by:
Speed = $ \dfrac{{{\text{Distance travelled}}}}{{{\text{Time taken}}}} $
Putting the value in above equation, we get
Time taken by A to cover 30 km is $ \dfrac{{30}}{x} $ km/hr.
Time taken by B to cover 30 km is $ \dfrac{{30}}{y} $ km/hr

According to the question, we can write:
   $ \Rightarrow $ $ \dfrac{{30}}{x} - \dfrac{{30}}{y} = 3 $
   $ \Rightarrow $ $ \dfrac{{10}}{x} - \dfrac{{10}}{y} = 1 $
  $ \Rightarrow $ $ \dfrac{{10}}{y} = \dfrac{{10}}{x} - 1 $ ..... (1)
If A double his speed then the speed of A is $ 2x $ km/hr
Therefore time taken by A to cover the 30 km is $ \dfrac{{30}}{{2x}} $ hr
Now according to the question,
   $ \Rightarrow $ $ \dfrac{{30}}{y} - \dfrac{{30}}{{2x}} = \dfrac{3}{2} $
   $ \Rightarrow $ $ \dfrac{{10}}{y} - \dfrac{{10}}{{2x}} = \dfrac{1}{2} $ ..... (2)
  Put the value of Eq (1) in Eq (2) we get,
 $ \Rightarrow $ $ \dfrac{{10}}{x} - 1 - \dfrac{{10}}{{2x}} = \dfrac{1}{2} $
 $ \Rightarrow $ $ \dfrac{{10}}{{2x}} = \dfrac{3}{2} $
  $ \Rightarrow $ $ x = \dfrac{{10}}{3} $ km/hr
Putting the value of x in Eq (1) we get,
  $ \Rightarrow $ $ \dfrac{{10}}{y} = \dfrac{{10}}{{\dfrac{{10}}{3}}} - 1 $
 $ \Rightarrow $ $ \dfrac{{10}}{y} = 3 - 1 $
   $ \Rightarrow $ $ y = \dfrac{{10}}{2} $
 $ \Rightarrow $ $ y = 5 $ km/hr
Hence, option C is correct.

Note:In this type of question, you should know the formula which relates speed with time and distance travelled. You should also know the formula to change km/hr to m/sec which is given as $ 1km/hr = \dfrac{5}{{18}}m/\sec $ , also $ 1m/\sec = \dfrac{{18}}{5}km/hr $ . You should also know how to solve the equation in two variables by representing one variable in terms of another and then putting it in another equation.