VeritasPrepKarishma wrote:

Yellow22 wrote:

How much time did it take a certain car to travel 400 km?

1) The car travelled the first 200 KM in 2.5 hrs?

2) If the Car's average speed was 20 KM per hour greater than it was, it would have travelled the 400 KM in 1 hour less time than it did.

I guess the solution is already clear to you.

Just for intellectual purposes, look at an alternative method:

If the car actually took t hours to cover 400 km, in the last 1 hour, the car travels a distance which is equal to 20*(t - 1) km

This must be the distance it covered in each hour since we are considering average speed.

400 = 20*(t - 1)*t

t(t - 1) = 20

t = 5 hrs

Nice one. Could't understand completely at first glance until I broke the equation down :

( Let original Avg Speed = X km/hr, Time taken = t hr., Distance = 400 km)

From statement 2,

=> (X+20) km/hr * (t-1) hr = 400 km

=> [ X km/hr * (t-1)hr ]+ [20 km/hr * (t-1)hr] = 400 km

=> [ X km/hr * (t-1)hr ]+ [20 *(t-1) km/hr * 1hr] = 400 km ---> Equation (1)

From the original problem statement, the car travels 400 km at X km/hr in t hrs

So if the car travels at X km/ hr , the distance covered in the first (t-1hrs) is given by [ X km/hr * (t-1)hr ]

and the distance covered in the last 1 hr is given by [20 *(t-1) km/hr * 1hr]

Hence speed in the last 1 hr = [20 *(t-1)] km/hr ( and this would be the avg speed for the entire distance of 400km)

[20 *(t-1)] km/hr * t hr = 400 km

Upon solving we get t= 5hrs.

Thanks Karishma.