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# Differential equations watch

1. A car travels a distance of 50km with an initial speed of 80km/hr. Given that the car's speed is proportional to the distance that remains to be covered, find the time to the nearest minute that the car takes to cover three-fifths of the distance.
2. (Original post by Htlee)
A car travels a distance of 50km with an initial speed of 80km/hr. Given that the car's speed is proportional to the distance that remains to be covered, find the time to the nearest minute that the car takes to cover three-fifths of the distance.
Work in the units given in the question so that distances are measured in km and times in hours and then you can ignore units until giving the answer.

Then, the car's speed being proportional to the distance that remains to be covered means that v=k(50-x) with k a constant of proportionality.
Can you solve it from there? Remember the definition of v in terms of x!

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Updated: February 11, 2018
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