A cyclist rides 30 km at an average speed of 9 km per hour. At what rate must the cyclist cover in the next 20 km in order to bring the overall average speed up to 10 km per hour?
+36916 30 km / 9 km / hr = 10 / 3 hr
(30 km + 20 km ) = 50 km 50 km / 10km/hr = 5 hours
5 - 10/3 = 5/ 3 hr to cover 20 km
20 km / 5/3 hr = 12 km / hr
+128475 The time for the cyclist to ride the first segment is 30 km / (9km / hr) = 30/9 hr = 10/3 hr
Call the rate that the cyclist must average in the second segment = R
The total time for the second segment = 20 km / R km / hr = (20/R) hr
The total distance traveled = 50 km
So
Total Distance / ( Total Time ) = Avg Rate
So
50 /(10/3 + 20/R) = 10
50 / 10 = (10/3 + 20/R)
5 = 10/3 + 20/R
5 - 10/3 = 20/R
5/3 = 20 / R
R = 20 / (5/3) = 20 * 3/5 = 60 / 5 = 12 km/ hr
