a man travels 600 kilometre partly by train and partly by car. if he covers 400 kilometre by train and the rest by car, it takes him 6 hours and 30 minutes .but if he travel 200 kilometre by train and rest by car he takes half an hour longer. find speed of train and that of car.
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Answer:
- speed of train = 100 km/h
- speed of Car = 80 km/h
Step-by-step explanation:
Let, speed of Train = x and speed of Car = y
Total distance to be covered is 600 km
then,
Using formula ; Time = distance / speed
- According to the first condition when person covers 400 km by train and rest by Car it takes him 6 hrs 30 min means 13/2 hours.
→ 400/x + 200/y = 13/2
- According to second condition when person covers 200 km by train and rest by Car he takes half an hour longer.
→ 200/x + 400/y = (13/2) + (1/2)
→ 200/x + 400/y = 14/2
→ 200/x + 400/y = 7
Now,
we have two linear equations in two variables as,
400/x + 200/y = 13/2 ...eqn(1)
and
200/x + 400/y = 7 ...eqn(2)
so,
Multiplying equation (1) by 2 both sides
→ 2(400/x) + 2(200/y) = 2(13/2)
→ 800/x + 400/y = 13 ...eqn(3)
subtracting equation (2) from equation (3) we will get,
→ 800/x - 200/x = 13 - 7
→ 600/x = 6
→ x = 600/6
→ x = 100 km/h
Putting value of x in eqn (2)
→ 200/x + 400/y = 7
→ 200/(100) + 400/y = 7
→ 2 + 400/y = 7
→ 400/y = 5
→ y = 80 km/h
Therefore,
- speed of train = 100 km/h
- speed of Car = 80 km/h.
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