Question

A bus travels at a certain average speed for a distance of 75 km and
then travels a distance of 90 km at an average speed of 10 km/hr
more than the first speed. If it takes 3 hours to complete the total journey, find its original speed.
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Answer 1

Let the original speed of the bus be x km/hr

Time taken to cover 75km = 75/x hrs.

New speed = (x + 10) km/hr

Time taken to cover 90 km with new speed = 90/(x + 10) hours

Total time taken to cover the whole journey = 3 hours.

According to the question,

$\dashrightarrow \sf \dfrac{75}{x} + \dfrac{90}{(x + 10)} = 3$

$\dashrightarrow \sf \dfrac{75(x + 10) + 90x}{x(x + 10)} = 3$

$\dashrightarrow \sf 75x + 750 + 90x = 3x(x + 10)$

$\dashrightarrow \sf 165x + 750 = {3x}^{2} + 30x$

$\dashrightarrow \sf {3x}^{2} - 135x - 750 = 0$

$\dashrightarrow \sf {x}^{2} - 45x - 250 = 0$

by splitting middle term,

$\dashrightarrow \sf {x}^{2} - 50x + 5x - 250 = 0$

$\dashrightarrow \sf x(x - 50) + 5(x - 50) = 0$

$\dashrightarrow \sf ( x + 5)(x - 50) = 0$

$\dashrightarrow \sf x - 50 = 0 \: (or) \: x + 5 = 0$

$\dashrightarrow \sf x = 50 \: (or) \: x = - 5$

The sleed can never be negative, thus the original speed of the bus was 50 km/hr