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A plane left 30 mins late …

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A plane left 30 mins late than its scheduled time and in order to reach the destination 1500km away in time it had to increase its speed by 100km/hr from the usual speed.Find its ususal speed
  • 1 answers

Sia ? 6 years, 6 months ago

Let usual speed = x km/hr
New speed = (x + 250)km/hr
Total distance = 1500 km
Time taken by usual speed = {tex}\frac{{1500}}{x}{/tex}hr
Time taken by new speed = {tex}\frac{{1500}}{{x + 250}}{/tex}hr
According to question,
{tex}\frac { 1500 } { x } - \frac { 1500 } { x + 250 } = \frac { 1 } { 2 }{/tex}
{tex}\Rightarrow \frac { 1500 x + 1500 \times 250 - 1500 x } { x ^ { 2 } + 250 x } = \frac { 1 } { 2 }{/tex}
{tex}\Rightarrow{/tex} x2 + 250x = 750000
{tex}\Rightarrow{/tex} x2 + 250x - 750000 = 0
{tex}\Rightarrow{/tex} x2 + 1000x - 750x - 750000 = 0
{tex}\Rightarrow{/tex} x(x + 1000) - 750(x + 1000) = 0
{tex}\Rightarrow{/tex} x = 750 or x = -1000
Therefore, usual speed is 750 km/hr, -1000 is neglected.

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