Question

# Shweta travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately. [4 MARKS]

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Solution

## Concept : 1 Mark Application : 1 Mark Calculation : 2 Marks Let the speed of the train be t km/hr and speed of the bus be b km/hr Then, Time taken by Shweta to travel by train is =60t [∵time=distspeed] Time taken by Shweta to travel by bus is =240b [∵ Remainimg distance = 300 km - 60 km] Total time taken is 4 hrs ⇒60t+240b=4……(i) Similarly 100t+200b=256……(ii) [∵4 hr 10 min=41060=256] Let 1t=x and 1b=y Then (i) reduces to, 60x+240y=4......(iii) (ii) reduces to , 100x+200y=256 ⇒4x+8y=16......(iv) 15×(iv)⇒ 60x+120y=52.....(v) Subtracting (v) from (iii) we get, 60x+240y−60x−120y=4−52 120y=32⇒y=180 ⇒1b=180 ⇒b=80 Substituting value of y in (iii) 60x+240(180)=4⇒x=160 ⇒1t=160 ⇒t=60 ∴t=60,b=80 ∴ The speed of the train is 60 km/hr and speed of the bus is 80 km/hr.

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