1) A journey of 240 km would take half an hour less if the speed were increased by 2 km/hr.
Find the usual speed.
Answers
Answer:
30 km/Hr
Step-by-step explanation:
A journey of 240 km would take half an hour less if the speed were increased by 2 km/hr.
Find the usual speed.
Let say Usual Speed = S km/Hr
Distance = 240 km
Time Taken = Distance /Speed
Time Taken with Usual speed = 240/S hr
increased speed = S + 2 km/hr
Time taken with increased speed = 240/(S +2) hr
240/S - 240/(S +2) = 1/2
Multiplying by 2S(S+2) both sides
480 ( S + 2 - S) = S² + 2S
=> S² + 2S - 960 = 0
=> S² + 32S - 30S -960 = 0
=> S(S + 32) -30(S -30) = 0
=> (S -30)(S +32) = 0
=> S = 30 (S ≠ - 32 as speed can not be -ve)
Usual speed = 30 km/Hr
Answer:30km/hr
Time =distance/speed
Let x be usual speed
time taken at usual speed=240/x
time taken when 2km/hr increased =240/x+2
Difference between the two time =1/2hr
240/x-240/x+2=1/2,on cross multiplying,
240x+480-240x/x^2+2x=1/2
On cross multiplying LHS and RHS,
960=x^2+2x or x^2+2x-960=0,by factorisation method
sum=+ve2,product =-ve 960
numbers:32 and (-30)
x^2+32x-30x-960=0
x(x+32)-30(x+32)=0
(x-30)(x+32)=0, as speed is a positive value,
x-30=0
x=30,therefore usual speed =30km/hr