Question

Rohit covered the distance of 340km in 5 hours by his cars. If the part of distance was at the speed of 60km/hr and rest at the 80km/hr.In how many hours did he travel at the 80km/hr.

Answer 1

let the distance travelled at 60km/h be x km and the time taken for that be t hrs; so distance travelled at 80km/h is (340 - x) km and time taken is (5 - t) hrs

speed = distance/time
60 = x/t ___ (i)
80 = (340-x)/(5-t) ___ (ii)

from (i): x = 60t
substituting x = 60t in (ii):
80 = (340 - 60t)/(5 - t)
400 - 80t = 340 - 60t
400 - 340 = 80t - 60t
60 = 20t
t = 3 [so 5-t = 2]
x = 60×3 = 180 [so 340-x = 160]

Rohit travelled 180 km at 60km/h in 3 hrs and 160 km at 80km/h in 2 hrs

Answer 2

Hit and trial method
60km/hr× 3hr= 180km.
80km/hr× 2hr= 160km.
Total-340 km.
Total time= 5hr.
This satisfies the conditions.
Hence Rohit traveled 80km/hr for 2 hours.

2nd method,
Let the time traveled by speed 60km/hr be x hours.
So distance= speed × time.
= 60*x=60x km.
Let the time traveled by speed 80km/hr be y hours.so distance= 80*y = 80y km.
Total distance= 340.
60x + 80y =340.
We have to put such value of x and y so that it satisfies the condition.
Putting x=3 and y= 2 satisfies the condition. 60×3 + 80×2.
180+160.
340.= RHS
Hence we can say Rohit traveled 80km/hr for 2 hours.
Hope you understand now.