Question

one third of a certain journey is covered at a rate of 25 km 1 km at a rate of 30 km per hour and the rest of the 50 km per hour what is the average speed for the whole journey​

Answer 1

Appropriate Question:-

One third of a certain journey is covered at the rate of 25 km/hour, one-fourth at the rate of 30 km/hour and the rest at 50 km/hour. What is the average speed for the whole journey?

Required Answer:-

Given:-

• One third of a certain journey is covered at the rate of 25 km/hour,
• One-fourth at the rate of 30 km/hour and the rest at 50 km/hour.

To Find:-

• The average speed for the whole journey.

Solution:-

Let the total distance be x.

As we were given,

• One third of a certain journey is covered at the rate of 25 km/hour,

Therefore,

-> Distance covered in 25km/hr = 1/3 × x = x/3

-> Distance covered in 30km/hr = 1/4 × x = x/4

-> Distance covered in 50km/hr = {1 - (1/3 + 1/4)} × x = 5/12 × x = 5x/12

Now,

$\\\bold{Total \: time \: taken = \dfrac{ \dfrac{x}{3}}{25} + \dfrac{ \dfrac{x}{4}}{30} +\dfrac{ \dfrac{5x}{12}}{50} }$

$\\ \sf{\implies{Total \: time\: taken = \dfrac{x}{75} + \dfrac{x}{120} + \dfrac{x}{120}}}$

$\\ \sf{\implies{Total \: time \: taken = \dfrac{x}{75} + \dfrac{x}{60} }}$

$\\ \sf{\implies{Total \: time \: taken = \dfrac{4x + 5x}{300} }}$

$\\ \sf{\implies{Total \: time \: taken = \bold{\frac{3x}{100}}}}$

Now, we know that:-

$\\ \underline{\boxed{\rm{Average \: speed = \dfrac{Total \: Distance}{Total \: time}}}}$

We have,

• Total distance = x
• Total time = 3x/100

Substituting the values:-

$\\ \bold{Average\: speed = \dfrac{x}{ \dfrac{3x}{100} } }$

$\\ \sf{\implies{Average \: speed = \frac{100}{3}}}$

$\\ \sf{\therefore{Average \: speed = \red{33 \dfrac{1}{3}km/hr} }}$

$\\ \underline{\rm{Hence, average \: speed \; for \: the \: hole \: journey \: is \: \green{33 \dfrac{1}{3} km/hr}}}$

Answer 2

33 1/3 km/hr

Explanation:-

Above answer ☝