Question

abdul travels 300km by train and 200km by taxi it takes him 5hrs 30mins . but if he travels 260km by train and 240km by taxi he takes 6mins longer find the speed of the train and the taxi

Answer 1

Let the speed of train be "x km/hr" and speed of taxi be "y km/hr"

here , distance travelled in both cases is same ,

Total distance = 300 + 200 = 260 + 240 = 500 km

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Case 1 :-

Time taken by train to travel 300 km = distance/speed

= 300/x

Time taken by taxi to travel 200 km = 200/y

so,

300/x + 200/y = 5.5 hour

Let 1/x = a , 1/y = b

300 a + 200 b =5.5 -----> (1)

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Case 2 :-

Time taken by train to travel 260 km = 260/x

Time taken by taxi to travel 240 km = 240/x

It is said , that , it took 6 min more ,

6min = 0.1 hour

time taken = 5.5 + 0.1 = 5.6 hours

so ,

260/x + 240/y = 5.6

260a + 240b = 5.6 ----> (2)

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Solving equations 1 and 2,

260a + 240b = 5.6 ---------> multiply by 5

300 a + 200 b =5.5 ---------> multiply by 6

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1300 a + 1200b = 28

1800a + 1200b = 33

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500a = 5

a = 5/500

= 1/100

260a + 240b = 5.6

260/100 + 240b = 5.6

2.6 + 240b = 5.6

240b = 3

b = 3/240

= 1/80

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we know that

1/a = x , 1/b = y

hence,

x = 100

y = 80

speed of train = 100 km/hr

speed of taxi = 80 km/hr