A man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But if he travels 130 km by train and the rest by car, it takes 18 minutes more. Find the speed of the train and that of the car.
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Let speed of train is x km/h
and speed of car is y km/h
a/c to question, if man covers 250km by train and (370 - 250) = 120km by car , it takes 4 hrs.
e.g., time taken by train + time taken by car = 4hrs
=> 250/x + 120/y = 4 ......... (i)
again, a/c to question, if man covers 130 km by train and (370-130)=240km by car, it takes 4hrs 18 minutes.
e.g., time taken by train + time taken by car =( 4 + 18/60)hrs [as you know, 18 minutes = 18/60 hr]
=> 130/x + 240/y = 43/10 ......(ii)
solving equations (i) and (ii),
2(250/x + 120/y) - (130/x + 240/y) = 2 × 4 - 43/10
=> 500/x - 130/x = 8 - 43/10 = (80 - 43)/10
=> (370)/x = 37/10
=> x = 100 km/h
put x in equation (i),
250/100 + 120/y = 4
=> 2.5 + 120/y = 4
=> 120/y = 1.5
=> y = 120/{3/2} = 240/3 = 80 km/h
hence, speed of train = 100km/h
and speed of car = 80 km/h
and speed of car is y km/h
a/c to question, if man covers 250km by train and (370 - 250) = 120km by car , it takes 4 hrs.
e.g., time taken by train + time taken by car = 4hrs
=> 250/x + 120/y = 4 ......... (i)
again, a/c to question, if man covers 130 km by train and (370-130)=240km by car, it takes 4hrs 18 minutes.
e.g., time taken by train + time taken by car =( 4 + 18/60)hrs [as you know, 18 minutes = 18/60 hr]
=> 130/x + 240/y = 43/10 ......(ii)
solving equations (i) and (ii),
2(250/x + 120/y) - (130/x + 240/y) = 2 × 4 - 43/10
=> 500/x - 130/x = 8 - 43/10 = (80 - 43)/10
=> (370)/x = 37/10
=> x = 100 km/h
put x in equation (i),
250/100 + 120/y = 4
=> 2.5 + 120/y = 4
=> 120/y = 1.5
=> y = 120/{3/2} = 240/3 = 80 km/h
hence, speed of train = 100km/h
and speed of car = 80 km/h
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