Kate is traveling on a bus for 730km. the bus is moving at an average speed of 100km. how long does Kate's journey take?
Answers
In such a problem it is interesting to guess the answer first and then see how it comes out. A logical guess would be the average of the two velocities or 16.5 km/hr. Now let us calculate it.
The trip from house to school takes 9km/18km/hr =1/2 hr and the return trip takes
9km/15km/hr = 3/5 hr. So the entire travel time is 1/2 + 3/5 = (5+6)/10 hr = 11/10 hr. We know the total trip is 18 km and to get the average speed we let x = average speed. So 11/10 = 18/x or x = 180/11 = 16.36 km/hr.
Interesting that the calculated is a bit less than the average. This can be explained by the slower velocity takes longer for the return trip so that the average is tilted a bit towards the slower velocity.
In such a problem it is interesting to guess the answer first and then see how it comes out. A logical guess would be the average of the two velocities or 16.5 km/hr. Now let us calculate it.
The trip from house to school takes 9km/18km/hr =1/2 hr and the return trip takes
9km/15km/hr = 3/5 hr. So the entire travel time is 1/2 + 3/5 = (5+6)/10 hr = 11/10 hr. We know the total trip is 18 km and to get the average speed we let x = average speed. So 11/10 = 18/x or x = 180/11 = 16.36 km/hr.
Interesting that the calculated is a bit less than the average. This can be explained by the slower velocity takes longer for the return trip so that the average is tilted a bit towards the slower velocity.