Question

Jake and paul each walk 10 km. the speed of jack is 1.5 faster than paul speed . what is the jake's speed ?

Answer 1

Let speed of Paul = x km/h
then , speed of Jack = (x + 1.5 ) km/h

a/c to question, Jack reaches the destination 1.5 hrs before Paul.
e.g., time taken by Jack + 1.5hrs = time taken by Paul

time taken by Jack = distance covered by Jack/speed of Jack
= 10km/(x + 1.5) hrs

time taken by Paul = distance covered by Paul/speed of Paul
= 10km/x hrs

now, 10/(x + 1.5) + 1.5 = 10/x

=> 1.5 = 10/x - 10/(x + 1.5)

=> 1.5 = 10{(x + 1.5 - x)}/x(x + 1.5)

=> 1.5 = 10 × 1.5/(x² + 1.5x)

=> x² + 1.5x = 10

=> x² + (3/2)x - 10 = 0

=> 2x² + 3x - 20 = 0

=> 2x² + 8x - 5x - 20 = 0

=> 2x(x + 4) -5(x + 4) = 0

=> (x + 4)(2x - 5) = 0

x = -4 , 5/2

hence, speed of Paul = 2.5 km/h
so, speed of Jack = x + 1.5 = 2.5 + 1.5 = 4 km/h