Layla traveled a total distance of $450 miles$ initially by car with an average speed of $60 miles/hour,$ and subsequently by train with an average speed of $110 miles/hour.$ Total time required is $5$ hours. Find the time spent on the train.

3

hours

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6

hours

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9

hours

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Solution

The correct option is A $3$ hours
Let the time traveled by car is $x hours,$ and by train is $y hours .$
$∴$ Distance covered by car $= x \times 60 miles$
And, distance covered by train $= y \times 110 miles$

Total distance covered $= 450 miles$
$∴ 60 x + 110 y = 450$
$\Rightarrow 6 x + 11 y = 45 . . . (a)$

Total time required $= 5$ hours
$∴ x + y = 5$
Multiply by $6$ in both sides.
$\Rightarrow 6 x + 6 y = 30 . . . (b)$

Subtract (b) from (a) to eliminate $6 x .$
$6 x + 11 y - (6 x + 6 y) = 45 - 30$
$\Rightarrow 11 y - 6 y = 15$
$\Rightarrow 5 y = 15$
$\Rightarrow y = 3$

$∴$ She spent $3$ hours on the train.

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Layla traveled a total distance of 450 miles initially by car with an average speed of 60 miles/hour, and subsequently by train with an average speed of 110 miles/hour. Total time required is 5 hours. Find the time spent on the train.

Layla traveled a total distance of $450 miles$ initially by car with an average speed of $60 miles/hour,$ and subsequently by train with an average speed of $110 miles/hour.$ Total time required is $5$ hours. Find the time spent on the train.