Question

A car travels a distance of 35 km with uniform speed. if the speed of the car is 2 km/hr less, it takes 2 hours more to cover the same distance. find the original speed of the car.

Answer 1

Hope u like my process
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Distance to travel = 35 km
Let the speed be x km/hr
Let time taken be y hr

Speed (x) = distance/time =35/y

If speed be 2 km/hr less than,
Speed would be =(x-2)km/hr
Time taken = (y+2)hrs

According to problem..
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Distance = speed × time

or, 35 = (x - 2)× (y +2)

$or. \: 35 = ( \frac{35}{y} - 2)(y + 2) \\ or. \: 35 = \frac{1}{y} (35 - 2y)(y + 2) \\ or. \: 35y = 35y - 2 {y}^{2} + 70 - 4y \\ or. \: 2 {y}^{2} + 4y - 70 = 0 \\ or. \: 2 {y}^{2} + 14y - 10y - 70 = 0 \\ or. \: 2y(y + 7) - 10(y + 7) = 0 \\ or. \: (2y - 10)(y + 7) = 0 \\ \\ either..y = \frac{10}{2} = 5 \: hrs \\ \\ or. \: y = - 7hrs \: \\ since \: time \: cannot \: be \: negative \\ \\ so \: y = 5hrs$
So the original speed of the car (x) =35/y
=35/5 = 7 km/hr

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