Question

(6) 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.

Answer 1

Answer:

Vishal travelled 150 km by bus.

Step-by-step explanation:

$let \: vishal \: travelled \: x \: km \: by \: bus \: and \: y \: km \: by \: plane \: \\ time \: = \frac{distance}{speed} \\ time \: taken \: by \: vishal \: while \: travelling \: by \: bus \: = \frac{x}{60} h \\ time \: taken \: by \: vishal \: while \: travelling \: by \: plane \: = \frac{x}{700} h \\ from \: the \: given \: conditions \: \\ x + y = 1900 \: \: ....(1) \\ and \: \frac{x}{60} + \frac{y}{700} = 5 \: ....(2) \\ multiplying \: equation \: (2) \: by \: 2100 \: the \: lcm \: of \: 60 \: and \: 700 \\ \frac{x}{60} \times 2100 + \frac{y}{700} \times 2100 = 5 \times 2100 \\ 35x + 3y = 10500 \: ....(3) \\ multiplying \: equation \: (1) \: by \: (3) \\ 3x + 3y = 5700 \: ...(4) \\ subtracting \: equation \: (4) \: from \: equation \: (3) \: \\ \: \: \: 35x + 3y = \: 10500 \: \: ...(3) \\ - \: 3x + 3y = \: 5700 \: \: ...(4) \\ - \: \: \: - \: \: \: \: \: \: \: \: \: \: - \\ 32x = \: 4800 \\ x = \frac{4800}{32} \\ x = 150$

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