More about equation

Question

Sam runs from town A to town B which are 20km apart. It is given that Sam runs with a constant speed in the first 12km,then his speed decreases by 5km/h in the last 8km. If the total time spent by Sam is 1hour and 8minutes ,find his speed in the first 12km.

Answer 1

8 minutes = 8/60 = 4/30 = 2/15 hour, so 1 hour 8 min = 17/15 hour

x is the speed on the 1st leg of the trip of 12 km.

t is the speed on the 2nd leg of the trip of 8 km.

12 = x( 17/15 - t) = (17/15)x - xt

8 = (x-5)(t) = xt - 5t

adding them together: 20 = (17/15)x - 5t

multiplies everything by 15:

300 = 17x - 75t

300 + 75t = 17x

(300 + 75t)/17 = x

(300 + 75t)/17 - 5 = x-5

(300 + 75t)/17 - 85/17 = x-5

(300 + 75t - 85)/ 17 = x - 5

(215 + 75t)/17 = x - 5

(215 + 75t)t/17 = (x-5)t = 8

(215 + 75t)t = 136

75t^2 + 215t - 136= 0

quadratic formula gives t = 8/15

per first equation:

12 = x( 17/15 - 815)

12 = x(9/15)

x = 12*15/9 = 180/9 = 20

CHECK:

He runs 20 km/hr for 9/15 hour ---> 20*9/15 = 180/15 = 12 km

He runs 15 km/hr for 8/15 hour ---> 15 * 8/15 = 8 km

BTW, 20 km/hr = 12.5 mph

Are you sure his name is Sam and not Flash Gordon?