Question

A man travels 500 km partly by train and partly by bus. He takes 5 hour 30 minutes,
if he travels 300 km by train and rest by bus. If he travels 260km by train and 240km
by bus, he takes 6 minutes longer. Find the speed of the train and bus separately.​

Answer 1

Solution:

Let, the speed of train be x & speed of bus be y.

T = d

-----

s

5.5 hour = 300/x + 200/y ------- (1)

5.6 hour = 260/x + 240/y ------- (2)

260-300/x + 240-200/y = 5.6-5.5 => 0.1 hr

-40/ x + 40/y = 0.1 hr

-40[ 1/x - 1/y] = 0.1 hr

1/x - 1/y = -0.1/40

1/x - 1/y = -0.1 × 10 /40 × 10 => -1/400

y-x/xy = -1/400

400(y-x)= -xy

400(y - x) + xy = 0

400 y - 400 x + xy = 0

400 y + xy = 400 x

y( 400+ x) = 400 x

y= (400 x/ 400+ x)

300/x + 200/y = 5.5×10/10 => 55/10

300/x + 200( 400+ x)/400x = 55/10

300/x + 400+x/2x = 55/10

600+400+x/2x = 55/10

10(1000) +10x = 55× 2x

10× 1000+10x = 110x

110x - 10 x= 10× 1000

100x = 10000

x= 100 km / hr

y = 400x/400+ x

y= 400× 100/400+100

y = 40000/500

y= 80 km / hr

SPEED OF TRAIN = 100 KM/ HR

SPEED OF BUS = 80 KM/HR

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