Difference between the time taken in covering a certain journey decreases by 45 min when the speed is increased from 10km/h to 20km/h .What is the difference between the time taken when the same distance is covered at a speed of 40km/h and 25 km/h ?
Answer please
Answers
Given:
The speed increases from 10 km/hr to 20 km/hr
Difference between the time taken to cover the journey decreases by 45 minutes.
To find:
The difference between the time taken when the same distance is covered at a speed of 40 km/hr and 25 km/hr
Formula to be used:
Time = Distance / Speed
Solution:
Finding the distance covered, when the speed is increased from 10 km/hr to 20 km/hr:
Let's assume
"D" = the distance covered during the certain journey
"S1" = 10 km/hr
"S2" = 20 km/hr
Difference between the time taken = 45 minutes
Using the formula of the speed, distance and time and substituting the given values, we get
[D/S1] - [D/S2] = 45/60
⇒ [D/10] - [D/20] = 3/4
⇒ D [(2 - 1) / 20] = 3/4
⇒ D [1/20] = 3/4
⇒ D = [3 × 20] / 4
⇒ D = 3 × 5
⇒ D = 15 km
Now,
Finding the difference between the time taken when the same distance is covered at a speed of 40 km/hr and 25 km/hr:
The distance covered = 15 km
S1 = 25 km/hr
S2 = 40 km/hr
∴ The difference in time taken is given,
= [15/25] - [15/40]
= [3/5] - [5/8]
= [24 - 15] / [40]
= [9/40] hr
= [9/40] × 60 ....... [∵ 1 hr = 60 minutes]
= [9 × 3] / 2
= 27/2
= 13.5 minutes
Thus, the difference between the time taken when the same distance is covered at a speed of 40km/h and 25 km/h is 13.5 minutes.
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The difference between the time taken when the same distance is covered at a speed of 40 km/h and 25 km/h is 13.5 minutes.
Step-by-step explanation:
Speed = S₁ = 10 km/hr
Speed = S₂ = 20 km/hr
Time difference between two speed = 45 min = 45/60 hr
Time = Distance/Speed
Time difference between two speed = 45/60 = D/10 - D/20
⇒ 45/60 = (2D - 1D)/20
⇒ 3/4 = D/20
∴ D = 60/4 = 15 km
Now,
Time difference between two speed = 15/25 - 15/40
Time difference between two speed = 3/5 - 5/8
Time difference between two speed = (24 - 15)/80
∴ Time difference between two speed = 9/80 × 60 = 13.5 min