Question

A A car starts from p for q travelling 20 kilometres an hour .1 and 1/2 hours later another Car starts from p travelling at the rate of 30 kilometres an hour and reaches q 2 and 1/2 hour before the first car. Find the distance from p to q

Answer 1

let the distance between P and Q = R

P =====T======================Q

first car start from P with speed 20 km/h
hence,
distance covered by first car =speed x time = 20 x (1+1/2 ) = 20 x 3/2 =30 km
now, 1st car reached at T

time taken by car from T to Q = distance b/w T to Q/speed
= (R-30)/20 hours

now, 2nd car start motion from P
and reached at Q (2 +1/2)h before the 1st car
time taken by 1st car to covered distance from T to Q - time taken by 2nd car to covered distance from P to Q = (2 + 1/2)=5/2

e.g
(R -30) /20 - R/30 =5/2

{3(R-30)-2(R)}/60 =5/2
(R-90) =150
R =150 +90
=240

hence,
distance between P and Q =240 km