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Question

A takes 3 hours more than B to walk 30 km. But, if A doubles his pace, he is ahead of B by 11/ 2 hours. Find their speed of walking

A
A's speed = 5km/hr, B's speed = 8 km/hr
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B
A's speed = 15/2km/hr, B's speed = 6 km/hr
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C
A's speed = 10/3km/hr, B's speed = 5 km/hr
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D
Data insufficient
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Solution

The correct option is C A's speed = 10/3km/hr, B's speed = 5 km/hr

Let the speed of A and B be x km/hr and y km/hr

Time taken by A to cover 30km 30xhrs

Time taken by B to cover 30km 30yhrs

According to the question

30x30y=3

10x10y=1...eq1

If A double his pace then the speed of A is 2x km/hr

therefore time taken by A to cover the 30 = 30/2xhrs And time taken by B to cover the 30KM = 30/yhrs


Now according to the question


30y302x=32


10y5x=12


10x+20y=1...eq2


Now we assume 1x=u and 1y=v


Putting the u and v in eq1 and eq 2 we get


10u10v=1...eq3


10u+20v=1...eq4


Adding eq3 and eq4 we get


10v=2


v=210


v=15=1y


y=5


Put v=15 in eq3


10u3=0


u=310=1x


x=103


Hence, the speed of A = 10\3 km/hr


The speed of B=5 km/hr respectively


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