Question

the speed of three runners a,b and c are in ratio 1:2:3. if A takes 2 hours more than C to cover a certain distance, find the time taken by B to cover the same distance.

Answer 1

let the distance 6y
and speed of a,b,c are x,2x,3x.
a takes 6y/x
b=6y/2x
c=6y/3x

6y/x-6y/3x=2
12y/3x=2
y/x=1/2

so b takes time=6y/2x=3×y/x=3/2 hours

Answer 2

Given,

The speed of three runners A, B, and C are in ratio 1:2:3.  A takes 2 hours more than C to cover a certain distance.

To find,

The time, taken by B to cover the same distance.

Solution,

• Suppose, the distance covered by the three runners is D.

• According to the given problem,

    ⇒  Speed of A = x, Speed of B = 2x, Speed of C = 3x.

• Let the time, taken by C cover distance D  = t hours.

• Then, the time taken by A to cover the same distance D is = (t +2) hours.

We know that,

Distance = Speed × Time

⇒   In the scenario of A ⇒   D = (x)(t+2).

⇒   In the scenario of C ⇒   D = (3x)(t)

⇒   Then,  tx + 2x = 3xt

⇒  t + 2 = 3t

⇒   2 = 2t

⇒   t = 1 hour.

Therefore, time is taken by C to cover, distance D = 1 hour.

Time taken, by A to cover distance D is t + 2 = 1 +2 = 3 hours.

• Now, let the time taken by B be t1.

   ⇒D =  (x)(3)  in the case of A.

   ⇒ D =  (2x)(t1) in the case of B.

   ⇒3x = 2x(t1)

   ⇒3 = 2(t1)

    t1= 1.5 hours.

Hence, Time taken by B to cover the distance D is 1.5 hours.