Question

Two men together start a journey in the same direction.they travel 9 kmph and 15 kmph respectively.after travelling for 6 hours the man travelling at 9kmph doubles his speed and both of them finish the distance in the same time.how many hours will they take to reach their destination

Answer 1

Let the total distance to be covered equals to S.

The distance covered in 6 hrs by each will be :

Let A be the one travelling at 9km/h and B be the one travelling at 15 km/h

Distance of A is : 6 × 9 = 54 km

Distance of B is : 15 × 6 = 90km

The distance remaining for A is : S - 54

For B is : S - 90

A doubles his speed and this becomes 2 × 9 = 18km/h

They will take the same time to reach their destination :

(S - 54) / 18 = (S - 90) / 15

15(S - 54) = (S - 90)18

15S - 810 = 18S - 1620

3S = 810

S = 270

Time = (270 - 90) / 15 = 12

The answer is 12 hrs.