SOLUTION: Jacob travelled 225 km to deliver goods from a factory. Had he travelled 15 kph more, he could make the trip in 1 ¼ hours less time and could have gone back to the factory earlier
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Question 697811: Jacob travelled 225 km to deliver goods from a factory. Had he travelled 15 kph more, he could make the trip in 1 ¼ hours less time and could have gone back to the factory earlier than usual. What is Jacob’s usual speed? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Jacob traveled 225 km to deliver goods from a factory.
Had he traveled 15 kph more, he could make the trip in 1 ¼ hours less time and could have gone back to the factory earlier than usual.
What is Jacob’s usual speed?
:
Let s = his usual speed
then
(s+15) = the faster speed
:
Write a time equation; time = dist/speed
:
Normal time - Faster time = 1.25 hrs - = 1.25
Multiply by s(s+15),resulting in:
225(s+15)- 225s = 1.25s(s+15)
225s + 3375 - 225s = 1.25s^2 + 18.75s
A quadratic equation
1.25s^2 + 18.75s - 3375 = 0
multiplying by 4 gets rid of the decimals, we have
5s^2 + 75s - 13500 = 0
now we can simplify this, divide by 5
s^2 + 15s - 2700 = 0
Factors to
(s-45)(s+60) = 0
the positive solution
s = 45 km/h is his usual speed
:
:
Confirm this by finding the time at each speed
225/45 = 5 hrs
225.60 = 3.75 hrs
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time dif:1.25 hrs
