Question : A car covers four successive 7 km distances at speeds of 10 km/h, 20 km/h, 30 km/h, and 60 km/h respectively. Its average speed over this distance is:
Option 1: 30 km/h
Option 2: 20 km/h
Option 3: 60 km/h
Option 4: 40 km/h
Correct Answer: 20 km/h
Solution :
Time taken to cover the first 7 km at 10 km/h = $\frac{7}{10}$ hour
Time taken to cover the second 7 km at 20 km/h =$\frac{7}{20}$ hour
Time taken to cover the third 7 km at 30 km/h = $\frac{7}{30}$ hour
Time taken to cover the fourth 7 km at 60 km/h =$\frac{7}{60}$ hour
Total time taken = $\frac{7}{10}$ + $\frac{7}{20}$+$\frac{7}{30}$ +$\frac{7}{60} =\frac{7}{5}$
Total distance covered = 4 $\times$ 7 = 28 km
$\text{Average speed}=\frac{\text{Total distance covered}}{{\text{Total time taken}}}$
$\text{Average speed}=\frac{\text{28}}{{\frac{7}{5}}}=20$ km/h
Hence, the correct answer is 20 km/h.
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