Question

★★100 points★★ , A challenge to all brainlics .
#MATH CHALLENGE

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

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.

Good question,

Here is your perfect answer!

Let speed be x(original),

1st case,

Distance = 75km,

speed = x,

Time = 75/x

2nd case,

Distance = 90km,

speed = x+10,

Time = 90/(x+10)

Total time = 3hr

=) 75/x + 90/(x+10) = 3

=) [ 75(x+10) + 90x] /x²+10x = 3

=) 75x + 750 + 90x = 3(x² + 10x)

=) 165x + 750 = 3x² + 30x

=) 0 = 3x² - 135x - 750

=) 0 = x² - 45x - 250

=) 0 = x² - 50x + 5x - 250

=) 0 = x(x-50) + 5(x-50)

=) 0 = (x+5) (x-50)

Hence x-50 = 0

=) x = 50 km/hr

Answer 2

▶ 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 .


▶ Answer :-

→ The original speed of the bus was 50 km/hr .


▶ Step-by-step explanation :-


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

→ Time taken to cover 75 km = $\sf \frac{75}{x}$ hours .

→ New speed = ( x + 10 ) km/hr .

→ Time taken to cover 90 km with new speed =
$\sf \frac{90}{x + 10 }$ hours .

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


$\sf \therefore \frac{75}{x} + \frac{90}{x + 10} = 3. \\ \\ \sf \implies \frac{75(x + 10) + 90x}{x(x + 10)} = 3. \\ \\ \sf \implies 165x + 750 = 3 {x}^{2} + 30x. \\ \\ \sf \implies 3 {x}^{2} - 135x - 750 = 0. \\ \\ \sf \implies {x}^{2} - 45x - 250 = 0. \\ \\ \sf \implies {x}^{2} - 50x + 5x - 250 = 0. \\ \\ \sf \implies x(x - 50) + 5(x - 50) = 0. \\ \\ \sf \implies (x - 50)(x + 5) = 0. \\ \\ \sf \implies x - 50 = 0. \: \: or \: \: x + 5 = 0. \\ \\ \sf \implies x = 50 \: \: or \: \: x = - 5. \\ \\ \huge \boxed{ \boxed{ \orange{\sf \implies x = 50.}}} \\ \\ \bigg( \sf \because speed \: cannot \: be \: negative. \bigg)$


✔✔ Hence, the original speed of the bus was 50 km/hr . ✅✅



$\huge \pink{ \boxed { \boxed{ \mathscr{THANKS}}}}$