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SOLUTION: An increase of speed of 4km/h on a journey of 32km reduces the time taken by 4 hours. find the orginal speed?
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Question 165552
:
An increase of speed of 4km/h on a journey of 32km reduces the time taken by 4 hours. find the orginal speed?
Answer by
ankor@dixie-net.com(18980)
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An increase of speed of 4km/h on a journey of 32km reduces the time taken
by 4 hours. find the original speed?
:
Let s = original speed
then
(s+4) = the faster speed
:
Write time equation; time =
:
original speed time - 4 hr = faster speed time
- 4 =
:
Multiply equation by s(s+4), results:
32(s+4) - 4s(s+4) = 32s
:
Multiply what's inside the brackets
32s + 128 - 4s^2 - 16s = 32s
:
-4s^2 - 16s + 128 = 0; subtracted 32s from both sides,
:
Simplify, change the signs, divide equation by -4
s^2 + 4s - 32 = 0
Factor
(s + 8)(s - 4) = 0
Positive solution
s = 4 km/hr is the original speed
:
:
Check solution finding the time of each (faster speed = 8 km/hr)
32/4 = 8 hrs
32/8 = 4 hrs
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differ 4 hrs