Seema goes to her office by scooter at a speed of \(\frac{25}{3}\) m/s and reaches 0.1 hour earlier. If she goes at a speed of 24 km/hr, she reaches office 5 minutes late. The distance (in km) of her office is:
22
Convert the first speed to km/hr: \(\frac{25}{3} \times \frac{18}{5} = 30\) km/hr. Let the distance be d km and the usual (scheduled) time be T hours.
At 30 km/hr she is 0.1 hour early: \(\frac{d}{30} = T - 0.1\). At 24 km/hr she is 5 minutes = \(\frac{1}{12}\) hour late: \(\frac{d}{24} = T + \frac{1}{12}\).
Subtracting, \(\frac{d}{24} - \frac{d}{30} = 0.1 + \frac{1}{12} = \frac{11}{60}\), and \(\frac{d}{24} - \frac{d}{30} = \frac{d}{120}\).
So \(\frac{d}{120} = \frac{11}{60}\), giving d = 22 km.
Check: 22/30 h = 44 min and 22/24 h = 55 min; the difference is 11 min, which equals 6 min (0.1 hour) early plus 5 min late. The data are consistent.
Hence, 22.
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Important Questions from Average Speed
A person covers a certain distance at the speed of 60 kmph and returns to the starting point at a speed of 40 kmph . Find the average speed (in km/hour) of the person for the whole journey.
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
A car has to cover 125 kms in 5 hours. What will be the average speed of the car if it has covered 90 kms in the first 3 hours?
A scooter from P to Q travels at 40 km/h and from Q to P at 30 km/h. What is the average speed of the scooter?
A car covers a distance of 100 km at a speed of 60 km/h and another 200 km at a speed of 75 km/h, what is the average speed of the car in km/h for the whole journey? (correct to one decimal place)
