Question

CLASS 10 - PAIR OF LINEAR EQUATION IN TWO VARIABLES

Answer 1

Let Length of journey = P km
original speed of train = Q km/h
original time taken to cover P km distance = T hour
hence,
T = P/Q -------(1)

A/C to question ,
(T - 4) hours = P/( Q + 6) -------(2)
(T + 6) hours = P/(Q - 6) ---------(3)

subtract eqn (3) - (2)
(T + 6) - (T - 4) = P { 1/(Q - 6) - 1/(Q + 6)}
10 = P { Q + 6 - Q + 6 }/(Q² - 36)
10 = 12P/(Q² - 36)
5(Q² - 36) = 6P ------(4)

now, put eqn (1) in eqn (2)
P/Q - 4 = P/(Q + 6)
P { 1/Q - 1/(Q + 6)} = 4
6P/(Q² + 6Q) = 4
6P = 4(Q² +6Q) ------(5)

from (4) and (5)
5(Q² - 36) = 4(Q² + 6Q)
5Q² - 180 = 4Q² + 24Q
Q² -24Q -180 = 0
Q = { 24 ±√(576 + 720)}/2
Q = { 24 ± 36}/2 = 30 km/h

put in eqn (4)
6P = 5(900 - 36)
6P = 5(864)
P = 5 × 144= 720 km

hence, Length of journey = 720 km