Yashvi rides a bicycle at a uniform speed. If the speed had been 4 km/hr more, it would have taken 1 hour less to travel 48 km distance. Determine her speed.
Answers
Step-by-step explanation:
Let yashvi's original speed be x km/hr and the time taken be y hrs
Distance=Speed×Time
A/Q
xy=48..........(i)
And
(x+4)×(y-1)=48.........(ii)
Therefore,
xy=(x+4)×(y-1)
xy=xy-x+4y-4
x-4y=-4
x=4y-4
x=4(y-1)
Put this value in eq(i)
4(y-1)y=48
y(y-1)=12
y²-y-12=0
y²-4y+3y-12=0
y(y-4)+3(y-4)=0
(y+3)(y-4)=0
y=-3 or 4
Since,time taken can't be negative.
Therefore,y=4 hrs
Putting this value in (i) we get
4x=48
x=12km/hr
Hence,Yashvi's original speed= 12 km/hr
Given : Yashvi rides a bicycle at a uniform speed.
If the speed had been 4 km/hr more, it would have taken 1 hour less to travel 48 km distance.
To Find : Determine the speed
Solution:
Let say Speed = S km/hr
Distance = 48 km
Time = Distance / Speed
Time Taken = 48/S hr
speed had been 4 km/hr more
=> Speed = S + 4 km/r
Time taken = 48/(S + 4)
Time Taken hour less = 48/S - 1
48/(S + 4) = 48/S - 1
=> 48S = 48(S + 4) - S(S + 4)
=> 48S = 48 + 192 - S² - 4S
=> S² + 4S - 192 = 0
=> S² + 16S - 12S - 192 = 0
=> S(S + 16) - 12(S + 16) = 0
=> (S - 12)(S + 16) = 0
=> S = 12 or S = - 16 ( not possible as Speed can not be negative )
Speed = 12 km/hr
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