Average Test-6 (Calculating average Speed)

Answer: Option B

Explanation

Given,

P=20 km, Q=15 km, R= 10km

X= 5km/h, Y= 3km, Z= 2km/h

∴ Required average speed=$\frac{P+Q+R}{{\displaystyle \frac{P}{X}+\frac{Q}{Y}+\frac{R}{Z}}}$

$$\begin{gathered} =\frac{20+15+10}{{\displaystyle \frac{20}{5}+\frac{15}{3}+\frac{10}{2}}} \\ =\frac{45}{4+5+5} \\ =\frac{45}{14} \\ =3\frac{3}{14}\mathrm{km}/\mathrm{h} \end{gathered}$$

Hence, Option B is correct.

Answer: Option A

Explanation

Given,

P=25%=$\frac{1}{4}$, Q=45%=$\frac{9}{20}$, R= 30%=$\frac{30}{100}=\frac{3}{10}$

X= 10 km/h, Y= 5 km/, Z= 15 km/h

∴ Required average speed=$\frac{1}{{\displaystyle \frac{P}{X}+\frac{Q}{Y}+\frac{R}{Z}}}$

$$\begin{gathered} =\frac{1}{{\displaystyle \frac{1}{4\times 10}}+{\displaystyle \frac{9}{20\times 5}}+{\displaystyle \frac{3}{10\times 15}}} \\ =\frac{1}{{\displaystyle \frac{1}{40}+\frac{9}{100}+\frac{1}{50}}} \\ =\frac{1}{{\displaystyle \frac{5+18+4}{200}}}=\frac{200}{27} \end{gathered}$$

= 7.40 km/hr

Hence, Option A is correct.

Answer: Option C

Explanation

Total distance covered by car =35+69

    =104 km/hr

Total time of the journey=45+75= 120minutes

= 2hr

Average speed of the car =$\frac{\mathrm{total} \mathrm{distance}}{\mathrm{total} \mathrm{time}}$

     =$\frac{104}{2}=52$ km/hr

Hence, Option C is correct.

Answer: Option D

Explanation

Total distance covered by the bus =39+25

   =64 km/hr

Total time taken to travel= $\left(\frac{45}{60}\right)\mathrm{hr}+\left(\frac{35}{60}\right)\mathrm{hr}=\frac{4}{3}\mathrm{hr}$

Average speed =$\frac{\mathrm{total} \mathrm{distance}}{\mathrm{total} \mathrm{time}}$

Average speed of the bus =$\frac{64}{{\displaystyle \left(\frac{4}{3}\right)}}$= 48 km/hr

Hence, Option D is correct.

Answer: Option B

Explanation

According to the question

We know the formula

Distance= Rate×time

Total distance =50×3+60×2

= 270

Total time =3+2=5

∴ Average speed =$\frac{\mathrm{Total} \mathrm{distance}}{\mathrm{Total} \mathrm{time}}$

$=\frac{270}{5}=54$ mph

Hence, Option B is correct.