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A man travels 450 km, in which 150 km is covered by car, 100 km by bus and rest of the journey by train. If the average speed of man for the whole journey is 75 km/hr and the ratio of the speed of car, bus and train is 3 : 2 : 4, then find the time in which he can complete the journey by bus alone?

A man travels 450 km, in which 150 km is covered by car, 100 km by bus and rest of the journey by train. If the average speed of man for the whole journey is 75 km/hr and the ratio of the speed of car, bus and train is 3 : 2 : 4, then find the time in which he can complete the journey by bus alone? Correct Answer 9 hr

Given:

Total distance is 450 km 

Distance covered by car is 150 km

Distance covered by bus is 100 km

Ratio of speed of car, bus and train is 3 : 2 : 4

Average speed = 75 km/hr

Formula used:

Average speed = Total distance/total time

Time = Distance/speed

Calculation:

Let, D = Total distance

D1 = Distance covered by car

D2 = Distance covered by bus

D3 = Distance covered by train

S1 = Speed of car

S2 = Speed of bus

S3 = Speed of train

Since D = 450 km

So, D3 = D - (D1 + D2)

⇒ D3 = 450 - (150 + 100) km

⇒ D3 = 200 km

Let the speed of car be 3x, bus be 2x and train be 4x.

Since, Average speed = Total distance/total time

So, 450/(150/3x + 100/2x + 200/4x) = 75

⇒ 450/(50/x + 50/x + 50/x) = 75

⇒ 450/(150/x) = 75

⇒ 3x = 75

⇒ x = 25

So, S2 = 2x

⇒ S2 = 2 × 25 km/hr

⇒ S2 = 50 km/hr

Now, time taken by bus to complete journey is 450/50 hr

∴ Time takes taken by bus to complete journey is 9 hr.

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