Question

a man Travels 370 km partly by train and partly by car if he covers 2:50 km by train and the rest by the car it takes him 4 hours but if he travels 1:30 km by train and rest by car he takes 18 minutes longer find the speed of the train and that of the car

Answer 1

Let speed of train and car be x and y resp

So we have Speed = Distance ÷ Time

Time taken 1st time by train = 250/ x

Time taken 1st time by car = 120/ y

So we get 250/x + 120/y = 4

Let a = 1/x and b = 1/y

So we have 250a + 120b = 4....(1)

Similarly, Time taken 2nd time by train = 130/x

Time taken 2nd time by car = 240/y

So we have, 130/x + 240/y = 4 hr 18 min

We can write, 130a + 240b = 4.3.....(2)   [18 min = 0.3 hr]

Solving (1) and (2) we have,

Multiplying eq.(1) by 2 and then subtracting it from eq.(2), we get

130a + 240b = 4.3

-500a - 240b = -8

-370a = -3.7

So, a = 0.01

Putting a in (1) we get

250(0.01) + 120b = 4

2.5 + 120b = 4

120b = 1.5

b = 0.0125

So 1/a = 1 / 0.01 = 100 kmph

1/b = 1 / 0.0125 = 80 kmph

Therefore speed of train is 100 kmph and that of car is 80 kmph.

Answer 2

Hello Dear.

Here is the answer---

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Let the Speed of the Train be a km/hr and the speed of the car be b km/hr.

In First Case,
Total Distance = 370 km.

For train  -)

Distance Traveled by the Train = 250 km.

Using the Formula,
 Time(T₁) = Distance/Speed
                = 250/a hrs.

Let 1/a be x.

⇒ T₁ = 250x hrs.

For Car -)

 Distance travelled by the Car = 370 - 250
                                                = 120 km.
Speed of the car = b km/hr.

Thus, time(T₂)  = 120/b hrs.

Let 1/b be y.
 ⇒ T₂ = 120y hrs.

As per as the Questions,

T₁ + T₂ = 4
250x + 120y = 4
⇒ 125x + 60y = 2  ----------eq(i)


In Second Case,

For the Train,

 Distance travelled by the Train = 130 km.
 
⇒ Time(T₃) = 130/a
                  = 130x hrs.

For the Car,

Distance travelled by the Car = 370 - 130
                                               = 240 km.

⇒ Time(T₄) = 240/b
                  = 240 y hrs.

As per as the Question,

       T₃ + T₄ = 4 hour + 18 min.
       130x + 240y = 4.3 hrs. -----eq(ii)


On Solving the eq(i) and (ii) Simultaneously,

We will get the Value of x = 0.01 and y = 0.0125

Thus, 1/a = x
   ⇒ a = 1/x
          = 1/0.01
          = 100 km/hr.


1/b = y
b = 1/y
b = 1/0.0125
   = 80 km/hr.


Speed of the Train = a km/hr
                               = 100 km/hr

Speed of the Car = b km/hr.
                            = 80 km/hr.


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Hope it helps.

Have a Marvelous Day.