an increase of speed of 4km/h on a journey of 32 km reduces the time taken by 4 hours find the original speed
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Let v be the original speed and t be the time taken in hours to complete the journey
Then,
v = 32 / t
t = 32 / v ………(1)
Also,
v + 4 = 32 / (t - 4)
v + 4 = 32 / [(32 / v) - 4] …………[∵ from equation (1)]
v + 4 = 32 / [(32 - 4v) / v]
v + 4 = 32v / (32 - 4v)
(v + 4) × (32 - 4v) = 32v
32v - 4v² + 128 - 16v = 32v
4v² + 16v - 128 = 0
On solving above equation we will get
v = 4 kmph or v = -8 kmph
Speed can’t be negative.
∴ Original speed is 4 kmph
Then,
v = 32 / t
t = 32 / v ………(1)
Also,
v + 4 = 32 / (t - 4)
v + 4 = 32 / [(32 / v) - 4] …………[∵ from equation (1)]
v + 4 = 32 / [(32 - 4v) / v]
v + 4 = 32v / (32 - 4v)
(v + 4) × (32 - 4v) = 32v
32v - 4v² + 128 - 16v = 32v
4v² + 16v - 128 = 0
On solving above equation we will get
v = 4 kmph or v = -8 kmph
Speed can’t be negative.
∴ Original speed is 4 kmph
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