a car covers first 30 km with a speed of 36 km per hour and the remaining journey with a speed of 54 km per hour.. if its average speed of the whole journey is 48 km per hour then find the total length of the journey..
Answers
Step-by-step explanation:
average speed = total distance / total time
=
t
1
+t
2
s
1
+s
2
=
36
x
+
54
x
x+x
=
x(
36
1
+
54
1
)
2x
=
(
108
5
)
2
=
5
216
=43.2km/h
Let's suppose the total length of the journey is "d" km.
According to the problem, the car covers the first 30 km with a speed of 36 km per hour. The time taken to cover this distance can be calculated as:
Time taken to cover the first 30 km = Distance ÷ Speed
Time taken to cover the first 30 km = 30 km ÷ 36 km/hour = 5/6 hour
For the remaining distance (d - 30) km, the car covers it with a speed of 54 km per hour. The time taken to cover this distance can be calculated as:
Time taken to cover the remaining (d - 30) km = Distance ÷ Speed
Time taken to cover the remaining (d - 30) km = (d - 30) km ÷ 54 km/hour = (d - 30)/54 hour
The average speed of the whole journey is given as 48 km per hour. We know that:
Average speed = Total distance ÷ Total time taken
Substituting the values of time taken for the two parts of the journey and the average speed, we get:
48 km/hour = d ÷ (5/6 + (d - 30)/54)
Simplifying the right-hand side:
48 km/hour = d ÷ (5/6 + d/54 - 5/2)
48 km/hour = d ÷ (d/54 + 1/3)
14400 = d ÷ (d/54 + 1/3)
Multiplying both sides by (d/54 + 1/3):
14400(d/54 + 1/3) = d
800d + 14400 = 54d
746d = 14400
d = 14400/746 ≈ 19.3 km
Therefore, the total length of the journey is approximately 19.3 km.