Average Test-6 (Calculating average Speed)

Answer: Option D

Explanation

According to the question,

A=20, B=30

we know the formula,

Average speed= $\frac{2\mathrm{AB}}{\text{A+B}}$

The average rate for the whole journey=$\frac{2\times 20\times 30}{20+30}$= 24 km/hr

Hence, Option D is correct.

Answer: Option A

Explanation

According to the question,

A=40, B=30, C=15

we know the formula,

Average speed during the whole journey = $\frac{3\mathrm{ABC}}{\text{AB+BC+CD}}$

The average rate for the whole journey

$$\begin{gathered} = \frac{3\times 40\times 30\times 15}{40\times 30+30\times 15+40\times 15} \\ =\frac{3\times 40\times 30\times 15}{2250} \end{gathered}$$

= 24 km/hr

Hence, Option A is correct.

Answer: Option A

Explanation

Let the total journeybe x km. Then $\frac{\mathrm{x}}{3}$km at the speed of 25 km/hr and $\frac{\mathrm{x}}{4}$km at 30 km/hr and the rest distance $\left(\mathrm{x}-\frac{\mathrm{x}}{3}-\frac{\mathrm{x}}{4}\right)=\frac{5}{12}\mathrm{x}$

at the speed of 50 km/hr.

Total time taken during the journey of x km

$$\begin{gathered} =\frac{\mathrm{x}}{3\times 25}\mathrm{hrs}+\frac{\mathrm{x}}{4\times 30}\mathrm{hrs}+\frac{5\mathrm{x}}{12\times 50}\mathrm{hrs} \\ =\frac{\mathrm{x}}{75}\mathrm{hrs}+\frac{\mathrm{x}}{120}\mathrm{hrs}+\frac{\mathrm{x}}{12\times 10}\mathrm{hrs} \\ =\frac{\mathrm{hrsx}}{75}+\frac{\mathrm{hrsx}}{120}+\frac{\mathrm{hrsx}}{120} \end{gathered}$$

(Expand the fraction to get the least common denominator)

$$\begin{gathered} =\frac{8\mathrm{hrsx}}{8\times 75}+\frac{5\mathrm{hrsx}}{5\times 120}+\frac{5\mathrm{hrs}}{5\times 120} \\ =\frac{8\mathrm{hrsx}+5\mathrm{hrsx}+5\mathrm{hrsx}}{600} \\ =\frac{18\mathrm{hrsx}}{600}=\frac{3}{100}\mathrm{hrsx} \end{gathered}$$

∴ Average speed =$\frac{\mathrm{x}}{{\displaystyle \frac{18\mathrm{x}}{600}}}=\frac{100}{3}=33\frac{1}{3}$ km/hr

Hence, Option A is correct.

Answer: Option C

Explanation

According to the question,

A=60, B=30

we know the formula,

Average speed= $\frac{2\mathrm{AB}}{\text{A+B}}$

The average speed = $\frac{2\times 60\times 30}{60+30}$=$\frac{3600}{90}$

= 40 km/hr

Hence, Option C is correct.

Answer: Option C

Explanation

According to the question,

A=60, B=30, C=10

we know the formula,

Average speed during the whole journey =$\frac{3\mathrm{ABC}}{\text{AB+BC+CD}}$

Average speed the whole journey

$$\begin{gathered} =\frac{3\times 60\times 30\times 10}{60\times 30+60\times 10+30\times 10} \\ =\frac{54000}{2700}= 20 \mathrm{km}/\mathrm{hr} \end{gathered}$$

Hence, Option C is correct.