Question

one third of a certain journey is covered at the rate of 25km/h, one fourth at the rate of 30km/h and the rest of 50km/h, what is the average speed for the whole journey?

Answer 1

d = total distance
t = total time
d/3 at 25
d/4 at 30
5d/12 at 50
-----------
t = (d/3)/25 + (d/4)/30 + (5d/12)/50


150t = 2d + 5d/4 + 5d/4 = 9d/2
300t = 9d
t = 3d/100
d = 100t/3
d/t = rate = 100/3
= 33 1/3 km/hr

Answer 2

Answer:

33.33k/h is the average speed of the whole journey

Step-by-step explanation:

Explanation:

Given , at the rate 25km/h $\frac{1}{3}$ of journey is covered .

at rate 30km/h , $\frac{1}{4}$ journey is covered .

and the rest journey is covered at rate 50 km/h .

Let , x km  be the total distance .

and let $T_1 , T_2 and T_3$ be   the time taken .

Step 1:

As we know the formula , Time = $\frac{Distance }{ Speed }$.

one third of a  journey is covered at rate of 25km/h

So distance = $\frac{x}{3}$

∴ $T_1 = \frac{\frac{x}{3} }{25}$ = $\frac{x}{75}$ hr

And one fourth covered at rate 30km/h

Distance = $\frac{x}{4}$

∴$T_2 = \frac{x}{120}$ hr

Now , the remaining distance = x - ($\frac{x}{3} +\frac{x}{4}$) = $\frac{5x}{12}$

∴$T_3 = \frac{\frac{5x}{12} }{50}$= $\frac{x}{120}$

Step 2:

Average speed = $\frac{Total \ distance \ travel }{Total \ time \ taken}$

⇒Average speed = $\frac{x}{\frac{x}{75} +\frac{x}{120} +\frac{x}{120} }$ = $\frac{600x }{8x +5x +5x}$ =  $\frac{600x}{18x}$ = 33.33 km/h

[Where lcm of 75,120and 120 is 600]

Final answer:

Hence , average speed for the whole journey is 33.33km/h

#SPJ2