Question

7.Jake and paul walk eachjake 10 km. Jake is 1.5 km faster than paul because of which he covers the distance in 1.5 hrs faster than paul. What is jakes 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 kmph