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in Linear Equations in Two Variables by (46.9k points)
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Out of 1900 km, Vishal travelled some distance by bus and some by aeroplane. Bus travels with average speed 60 km/hr and the average speed of aeroplane is 700 km/hr. It takes 5 hours to complete the journey. Find the distance Vishal travelled by bus.

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Best answer

Let the distance Vishal travelled by bus be x km and by aeroplane be y km.

According to the first condition,

x + y = 1900 …(i)

Time = \(\frac{Distance}{Speed}\)

∴ Time required to cover x km by bus = \(\frac{x}{60}\) hr

    Time required to cover y km  by aeroplane =   \(\frac{y}{700}\) hr

According to the second condition

      \(\frac{x}{60}\) + \(\frac{y}{700}\) = 5

∴  \(\frac{700x + 60 y}{60 X 700 }\) = 5

∴   700x + 60y = 5 x 60 x 700

∴   70x + 6y = 21000      ......(iii)  [ Dividing both sides by 10 ]

Multiplying equation (i) by 6, we get

6x + 6y= 11400 …(iii)

Subtracting equation (iii) from (ii), we get

∴           x = \(\frac{9600}{64}\)

∴           x = 150

∴ The distance Vishal travelled by bus is 150 km.

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