Ashutosh can cover a certain distance in 84 min by covering 2/3 of distance at 4 km/h and the rest at 5 km/h . find the total distance.
Answers
Answer:
The total distance = 6 km
Step-by-step explanation:
Speed = Distance / Time
Distance = Speed x Time
Total distance = d
Total time = 84 minutes = (84/60) hours = 1.4 hours
Part 1 of journey
Speed = 4 km per hour
Time = t hours
Distance = (2/3)*d
Distance = Speed x Time
=> 2d/3 = 4t
=> 2d = 12t
=> d = 6t .......(Eqn 1)
Part 2 of journey
Speed = 5 km per hour
Time = (1.4 - t) hours ..because total time = 1.4 hours
Distance = (1/3)*d ..because 2/3 of distance is covered in Part 1
Distance = Speed x Time
=> d/3 = 5(1.4 - t)
=> d = 15(1.4 - t)
=> d = 21 - 15t .......(Eqn 2)
Using Eqn 1 in Eqn 2,
6t = 21 - 15t
=> 21t = 21
=> t = 1
Using (Eqn 1), we get:
d = 6*1
=> d = 6 km
Total distance = 6 km
Verification:
Part 1
Distance = (2/3)*6 = 4
Time = t = 1 hour
Speed = 4 km per hour ....(Verified)
Part 2
Distance = (1/3)*6 = 2
Time = 1.4 - t = 1.4 - 1 = 0.4 hours
Speed = 2/0.4 = 5 km per hour ..(Verified)
Answer:
x = 42/7 x = 6km this is the answer