Two planes start from a city and fly in opposite directions, one averaging a speed of $40$ kmph greater than the second.If they are $3400$ km apart after $5$ hours, find their average speeds.

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Solution

Let the speed of one plane be $x$ kmphr

Then the speed of other plane is $x + 40$ kmphr

Distance travelled by first plane in $5$ hrs $= s p e e d \times t i m e = x \times 5 = 5 x$

Distance travelled by second plane in $5$ hrs $= (x + 40) \times 5$

Distance traveled by first plane $+$ Distance traveled by other plane $= 3400$ km

$\Rightarrow 5 x + 5 (x + 40) = 3400$

$\Rightarrow 5 x + 5 x + 200 = 3400$

$\Rightarrow 10 x = 3400 - 200 = 3200$

$\Rightarrow x = \frac{3200}{10} = 320$ kmphr

Speed of first plane $= x$ kmphr $= 320$ kmphr

Speed of second plane $= x + 40 = 320 + 40 = 360$ kmphr

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Two planes start from a city and fly in opposite directions, one averaging a speed of 40kmph greater than the second.If they are 3400km apart after 5 hours, find their average speeds.

Two planes start from a city and fly in opposite directions, one averaging a speed of $40$ kmph greater than the second.If they are $3400$ km apart after $5$ hours, find their average speeds.