A man travels 600km apart by train and partly by car. It takes 8 hours and 40 minutes if he travels 320 km by train and rest by car. It would take 30 minutes more if he travels 200 km by train and the rest by the car/. Find the speed of the train and by car separately.
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Answers
EXPLANATION.
A man travels 600 km apart by train and partly by car.
It takes 8 hours 40 minutes if he travels 320 km by train and rest by car.
It would take 30 minutes more.
If he travels 200 km by train and the rest by the car.
As we know that,
Distance = speed x time.
speed = Distance/Time.
Time = Distance/speed.
Total distance travelled by man = 600 km.
Distance travelled by train + Distance travelled by car = 600 km.
320 km + Distance travelled by car = 600 km.
Distance travelled by car = 600 km - 320 km = 280 km.
Now,
Let, we assume that,
Speed of train be = x.
Speed of car be = y.
Time taken by man to travelled 320 km by train = 320/x.
Time taken by man to travelled 280 km by train = 280/y.
Total time taken by man to travel 600 km is,
⇒ (320)/x + (280)/y = 8 hours 40 minutes.
⇒ (320)/x + (280)/y = 8(40/60).
⇒ (320)/x + (280)/y = 8(2/3).
⇒ (320)/x + (280)/y = 26/3. - - - - - (1).
Distance travelled by train + Distance travelled by car = 600 km.
⇒ 200 km + Distance travelled by car = 600 km.
Distance travelled by car = 600 km - 200 km = 400 km.
Time taken by man to travelled 200 km by train = 200/x.
Time taken by man to travelled 400 km by train = 400/y.
Total time taken by man to travel 600 km is,
⇒ (200)/x + (400)/y = 26/3 + 30 minutes.
⇒ (200)/x + (400)/y = 26/3 + 1/2.
⇒ (200)/x + (400)/y = 55/6. - - - - - (2).
We obtained two equation, we get.
⇒ (320)/x + (280)/y = 26/3. - - - - - (1).
⇒ (200)/x + (400)/y = 55/6. - - - - - (2).
As we know that,
Let we assume that,
⇒ 1/x = a and 1/y = b.
We can write equation as,
⇒ 320a + 280b = 26/3. - - - - - (3).
⇒ 960a + 840b = 26. - - - - - (3).
⇒ 200a + 400b = 55/6. - - - - - (4).
⇒ 1200a + 2400b = 55. - - - - - (4).
Multiply equation (3) by 5.
Multiply equation (4) by 4.
⇒ 960a + 840b = 26. - - - - - (3). x 5.
⇒ 1200a + 2400b = 55. - - - - - (4). x 4.
⇒ 4800a + 4200b = 130. - - - - - (3).
⇒ 4800a + 9600b = 220. - - - - - (4).
Subtract both equations (3) and (4), we get.
⇒ 4800a + 4200b = 130. - - - - - (3).
⇒ 4800a + 9600b = 220. - - - - - (4).
⇒ - - -
We get,
⇒ 5400b = 90.
⇒ 60b = 1.
⇒ b = 1/60,
Put the value of b = 1/60 in equation (3), we get.
⇒ 960a + 840b = 26. - - - - - (3).
⇒ 960a + 840 x (1/60) = 26.
⇒ 960a + 14 = 26.
⇒ 960a = 12.
⇒ 80a = 1.
⇒ a = 1/80.
We assume that,
⇒ 1/x = a.
⇒ 1/x = 1/80.
⇒ x = 80.
⇒ 1/y = b.
⇒ 1/y = 1/60.
⇒ y = 60.
Speed of train be = x = 80 km/hr.
Speed of car be = y = 60 km/hr.