SOLUTION: I can't come up with a suitable formula to solve this question please help. In a certain number of hours, a woman travelled 36km. If she had travelled 1.5 km/h faster, it would ha

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Question 426496: I can't come up with a suitable formula to solve this question please help.
In a certain number of hours, a woman travelled 36km. If she had travelled 1.5 km/h faster, it would have taken 3 hrs less to make the journey. how many kilometers did she travel per hour.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = number of hours to travel the 36 km
Let s = the speed to travel the 36 km
So s = 36/t
We can represent 1.5 km/h faster as: s + 1.5
And 3 hrs less as t - 3
So we need to solve
s + 1.5 = 36/(t - 3)
Using the value for s above we can write
36/t + 1.5 = 36/(t - 3)
Multiply through by t:
36 + 1.5t = 36t/(t - 3)
Now multiply both sides by t - 3:
(t - 3)(36 + 1.5t) = 36t
Solve for t:
36t + 1.5t^2 - 108 - 4.5t = 36t -> 1.5t^2 - 4.5t - 108 = 0
So, t = (4.5 +- sqrt(4.5^2 - (4)(1.5)(-108)))/(2*1.5)
This gives t = 10.1168 hrs.
Therefore her speed in km/hr = 36/10.1168 = 3.558 km/hr