Time, Distance and Speed

Answer :

Distance covered by 1st man at S km/hr = X km

Time taken by him = t hours.

Therefore, Speed = S = X/t km/hr.

Distance covered by 2nd man at R km/hr = X/2 km

Time taken by him = 2t hours.

Therefore, Speed = R = (X/2)/2t km/hr = X/4t km/hr.

Required ratio = S:R = X/t : X/4t = 1 : 1/4 = 4:1.

Answer :

Initial speed of the cyclist = 7km/hr.

Distance covered in 1st 3 hours = 7 x 3 = 21 km.

After increasing, 1km/hr for every 3 hours period,

Distance covered in 2nd 3 hours period = 8 x 3 = 24 km.

Distance covered in 3rd 3 hours period = 9 x 3 = 27 km.

Distance covered in 4th 3 hours period = 10 x 3 = 30 km.

Total distance covered = 21 + 24 + 27 + 30 = 102 km.

Remaining km to cover = 113 - 102 = 11 km.

Speed in 5th 3 hours period = 11 km/hr.

Time to cover 13 km at 11km/hr = 11/11 hours = 1 hour.

Now, the total time taken by him for 113 km = (3 + 3 + 3 + 3 + 1) = 13 hours.

Answer :

Speed of the rider = 60km/hr.

Distance covered in 1st 2 hours = 60 km.

He increased his speed in every 2 hours by 3 km/hr.

Distance covered in every 2 hours will be, 60, 63, 66,... upto 12 terms.(for 24 hours).

The above series is an A.P series;

Sum of first n terms = (n/2)(2a+(n-1)d)

Here, a = 60, d = 3 and n = 12.

Sum of first 12 terms = (12/2)(2(60)+(11)3) = 6(120 + 33) = 6(153) = 918.

Hence, he covers 918 km in 24 hours.

Answer :

Initial speed of the car = 50km/hr

Due to engine problem, speed is reduced to 10km for every 2 hours(i.e., 5 km per hour).

Speed of the car at 11 am = (50 - 5) = 45km/hr

Time to cover 10 km at 45 km/hr = distance/speed = 10/45 hours. = 2/9 hours

= 2/9 x 60 minutes = 40/3 minutes = 13 minutes + 1/3 minutes

= 13 minutes + 1/3 x 60 seconds

= 13 minutes and 20 seconds.

Answer :

Speed = (600 / (5*60)) m/sec

           = 2 m/sec

Converting m/sec to km/hr

2*(5/18)= 7.2 km/hr